Sr Examen

Lang:

Otras calculadoras

¿Cómo usar?
Gráfico de la función y =:
x^2*e^(2-x)
x^3-12*x+5
x^2-9*x+14
-x^2+6*x-4
Expresiones idénticas
x^ tres + dos *x+ uno /(x-(uno / diez))*(x^ dos +x+(uno / dos))
x al cubo más 2 multiplicar por x más 1 dividir por (x menos (1 dividir por 10)) multiplicar por (x al cuadrado más x más (1 dividir por 2))
x en el grado tres más dos multiplicar por x más uno dividir por (x menos (uno dividir por diez)) multiplicar por (x en el grado dos más x más (uno dividir por dos))
x3+2*x+1/(x-(1/10))*(x2+x+(1/2))
x3+2*x+1/x-1/10*x2+x+1/2
x³+2*x+1/(x-(1/10))*(x²+x+(1/2))
x en el grado 3+2*x+1/(x-(1/10))*(x en el grado 2+x+(1/2))
x^3+2x+1/(x-(1/10))(x^2+x+(1/2))
x3+2x+1/(x-(1/10))(x2+x+(1/2))
x3+2x+1/x-1/10x2+x+1/2
x^3+2x+1/x-1/10x^2+x+1/2
x^3+2*x+1 dividir por (x-(1 dividir por 10))*(x^2+x+(1 dividir por 2))
Expresiones semejantes
x^3+2*x-1/(x-(1/10))*(x^2+x+(1/2))
x^3-2*x+1/(x-(1/10))*(x^2+x+(1/2))
x^3+2*x+1/(x-(1/10))*(x^2-x+(1/2))
x^3+2*x+1/(x-(1/10))*(x^2+x-(1/2))
x^3+2*x+1/(x+(1/10))*(x^2+x+(1/2))

Trazado el gráfico de la función/ x^3+2*x+1/(x-(1/10))*(x^2+x+(1/2))

Gráfico de la función y = x^3+2x+1/(x-(1/10))(x^2+x+(1/2))

Solución

Ha introducido [src]

                   2       1
                  x  + x + -
        3                  2
f(x) = x  + 2*x + ----------
                   x - 1/10

f{\left(x \right)} = \left(x^{3} + 2 x\right) + \frac{\left(x^{2} + x\right) + \frac{1}{2}}{x - \frac{1}{10}}

f = x^3 + 2*x + (x^2 + x + 1/2)/(x - 1/10)

Gráfico de la función

Dominio de definición de la función

Puntos en los que la función no está definida exactamente:

x_{1} = 0.1

Puntos de cruce con el eje de coordenadas X

El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:

\left(x^{3} + 2 x\right) + \frac{\left(x^{2} + x\right) + \frac{1}{2}}{x - \frac{1}{10}} = 0

Resolvermos esta ecuación
Solución no hallada,
puede ser que el gráfico no cruce el eje X

Puntos de cruce con el eje de coordenadas Y

El gráfico cruce el eje Y cuando x es igual a 0:
sustituimos x = 0 en x^3 + 2*x + (x^2 + x + 1/2)/(x - 1/10).

\frac{0^{2} + \frac{1}{2}}{- \frac{1}{10}} + \left(0^{3} + 0 \cdot 2\right)

Resultado:

f{\left(0 \right)} = -5

Punto:

(0, -5)

Extremos de la función

Para hallar los extremos hay que resolver la ecuación

\frac{d}{d x} f{\left(x \right)} = 0

(la derivada es igual a cero),
y las raíces de esta ecuación serán los extremos de esta función:

\frac{d}{d x} f{\left(x \right)} =

primera derivada

3 x^{2} + 2 + \frac{2 x + 1}{x - \frac{1}{10}} - \frac{\left(x^{2} + x\right) + \frac{1}{2}}{\left(x - \frac{1}{10}\right)^{2}} = 0

Resolvermos esta ecuación
Raíces de esta ecuación

x_{1} = \frac{\sqrt{- \frac{199}{300} - \frac{4733}{60000 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}} + 2 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}}}{2} + \frac{1}{20} + \frac{\sqrt{- \frac{199}{150} - 2 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}} + \frac{4733}{60000 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}} + \frac{1}{5 \sqrt{- \frac{199}{300} - \frac{4733}{60000 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}} + 2 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}}}}}{2}

x_{2} = - \frac{\sqrt{- \frac{199}{150} - 2 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}} + \frac{4733}{60000 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}} + \frac{1}{5 \sqrt{- \frac{199}{300} - \frac{4733}{60000 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}} + 2 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}}}}}{2} + \frac{\sqrt{- \frac{199}{300} - \frac{4733}{60000 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}} + 2 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}}}{2} + \frac{1}{20}

Signos de extremos en los puntos:

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       2                                                                                                                                                                                                                                                                                                                    
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                /                                                                                                                        _____________________________________________________________________________________________________________________________________________________________________________________________\                                                                                                                       _____________________________________________________________________________________________________________________________________________________________________________________________ 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        3                                                                                                                                                                                                                       |                                                                                                                       /                ____________________________                                                                                                                                                 |                                                                                                                      /                ____________________________                                                                                                                                                  
                                                                                                                         _____________________________________________________________________________________________________________________________________________________________________________________________                                                                                                           /                                                                                                                        _____________________________________________________________________________________________________________________________________________________________________________________________\                                                                                                                                                                                                                        |                                                                                                                      /                /               ____________                                                                                                                                                  |                                                                                                                     /                /               ____________                                                                                                                                                   
                                                                                                                        /                ____________________________                                                                                                                                                                                                                                                            |                                                                                                                       /                ____________________________                                                                                                                                                 |                                                                                                                                                                                                                        |                                                                                                                     /     199        /   8313701    \/ 1799507686                                                      1                                                                      4733                  |                                                                                                                    /     199        /   8313701    \/ 1799507686                                                      1                                                                      4733                   
                                                                                                                       /                /               ____________                                                                                                                                                                                                                                                             |                                                                                                                      /                /               ____________                                                                                                                                                  |                                                                                                                                                                                                                        |                                                                                                                    /    - --- - 2*3 /   --------- + --------------  + --------------------------------------------------------------------------------------------------- + --------------------------------------- |                                                                                                                   /    - --- - 2*3 /   --------- + --------------  + --------------------------------------------------------------------------------------------------- + ---------------------------------------  
                                                                                                                      /     199        /   8313701    \/ 1799507686                                                      1                                                                      4733                                                                                                                             |                                                                                                                     /     199        /   8313701    \/ 1799507686                                                      1                                                                      4733                  |                                                                                                                                                                                                                        |               _______________________________________________________________________________________             /       150     \/    216000000      1080000                    _______________________________________________________________________________________              ____________________________ |              _______________________________________________________________________________________             /       150     \/    216000000      1080000                    _______________________________________________________________________________________              ____________________________  
                                                                                                                     /    - --- - 2*3 /   --------- + --------------  + --------------------------------------------------------------------------------------------------- + ---------------------------------------                                                                                                            |                                                                                                                    /    - --- - 2*3 /   --------- + --------------  + --------------------------------------------------------------------------------------------------- + --------------------------------------- |                                                                                                                                                                                                                        |              /                ____________________________                                                       /                                                               /                ____________________________                                                        /               ____________  |             /                ____________________________                                                       /                                                               /                ____________________________                                                        /               ____________   
                _______________________________________________________________________________________             /       150     \/    216000000      1080000                    _______________________________________________________________________________________              ____________________________                                                                                                            |               _______________________________________________________________________________________             /       150     \/    216000000      1080000                    _______________________________________________________________________________________              ____________________________ |                                                                                                                                                                                                                        |             /                /               ____________                                                       /                                                               /                /               ____________                                                        /   8313701    \/ 1799507686   |            /                /               ____________                                                       /                                                               /                /               ____________                                                        /   8313701    \/ 1799507686    
               /                ____________________________                                                       /                                                               /                ____________________________                                                        /               ____________                                                                                                             |              /                ____________________________                                                       /                                                               /                ____________________________                                                        /               ____________  |                                                                                                                                                                                                                        |            /     199        /   8313701    \/ 1799507686                       4733                            /                                                               /     199        /   8313701    \/ 1799507686                       4733                     60000*3 /   --------- + --------------  |           /     199        /   8313701    \/ 1799507686                       4733                            /                                                               /     199        /   8313701    \/ 1799507686                       4733                     60000*3 /   --------- + --------------   
              /                /               ____________                                                       /                                                               /                /               ____________                                                        /   8313701    \/ 1799507686                                                                                                              |             /                /               ____________                                                       /                                                               /                /               ____________                                                        /   8313701    \/ 1799507686   |                                                                                                                                                                                                                        |           /    - --- + 2*3 /   --------- + --------------  - ---------------------------------------          /                                                       5*      /    - --- + 2*3 /   --------- + --------------  - ---------------------------------------          \/    216000000      1080000      |          /    - --- + 2*3 /   --------- + --------------  - ---------------------------------------          /                                                       5*      /    - --- + 2*3 /   --------- + --------------  - ---------------------------------------          \/    216000000      1080000       
             /     199        /   8313701    \/ 1799507686                       4733                            /                                                               /     199        /   8313701    \/ 1799507686                       4733                     60000*3 /   --------- + --------------                                                                                                             |            /     199        /   8313701    \/ 1799507686                       4733                            /                                                               /     199        /   8313701    \/ 1799507686                       4733                     60000*3 /   --------- + --------------  |                                                                                                                                                                                                                        |          /       300     \/    216000000      1080000                   ____________________________         /                                                               /       300     \/    216000000      1080000                   ____________________________                                            |         /       300     \/    216000000      1080000                   ____________________________         /                                                               /       300     \/    216000000      1080000                   ____________________________                                             
            /    - --- + 2*3 /   --------- + --------------  - ---------------------------------------          /                                                       5*      /    - --- + 2*3 /   --------- + --------------  - ---------------------------------------          \/    216000000      1080000                                                                                                                 |           /    - --- + 2*3 /   --------- + --------------  - ---------------------------------------          /                                                       5*      /    - --- + 2*3 /   --------- + --------------  - ---------------------------------------          \/    216000000      1080000      |                                                                                                                                                                                                                        |         /                                                              /               ____________         /                                                               /                                                              /               ____________                                             |        /                                                              /               ____________         /                                                               /                                                              /               ____________                                              
           /       300     \/    216000000      1080000                   ____________________________         /                                                               /       300     \/    216000000      1080000                   ____________________________                                                                                                                                                       |          /       300     \/    216000000      1080000                   ____________________________         /                                                               /       300     \/    216000000      1080000                   ____________________________                                            |                                                                                                                                                                                                                        |        /                                                              /   8313701    \/ 1799507686         /                                                               /                                                              /   8313701    \/ 1799507686                                              |       /                                                              /   8313701    \/ 1799507686         /                                                               /                                                              /   8313701    \/ 1799507686                                               
          /                                                              /               ____________         /                                                               /                                                              /               ____________                                                              _______________________________________________________________________________________   |         /                                                              /               ____________         /                                                               /                                                              /               ____________                                             |                   _____________________________________________________________________________________________________________________________________________________________________________________________        |       /                                                      60000*3 /   --------- + --------------       /                                                               /                                                      60000*3 /   --------- + --------------                                             |      /                                                      60000*3 /   --------- + --------------       /                                                               /                                                      60000*3 /   --------- + --------------                                              
         /                                                              /   8313701    \/ 1799507686         /                                                               /                                                              /   8313701    \/ 1799507686                                                              /                ____________________________                                              |        /                                                              /   8313701    \/ 1799507686         /                                                               /                                                              /   8313701    \/ 1799507686                                              |                  /                ____________________________                                                                                                                                                    11   |1    \/                                                             \/    216000000      1080000         \/                                                              \/                                                             \/    216000000      1080000                                                 |    \/                                                             \/    216000000      1080000         \/                                                              \/                                                             \/    216000000      1080000                                                  
        /                                                      60000*3 /   --------- + --------------       /                                                               /                                                      60000*3 /   --------- + --------------                                                            /                /               ____________                                               |       /                                                      60000*3 /   --------- + --------------       /                                                               /                                                      60000*3 /   --------- + --------------                                             |                 /                /               ____________                                                                                                                                                     -- + |-- + ------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|  + ------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 
 1    \/                                                             \/    216000000      1080000         \/                                                              \/                                                             \/    216000000      1080000                                                   1           /     199        /   8313701    \/ 1799507686                       4733                     |1    \/                                                             \/    216000000      1080000         \/                                                              \/                                                             \/    216000000      1080000                                                 |                /     199        /   8313701    \/ 1799507686                                                      1                                                                      4733                     20   \20                                                   2                                                                                                                                                        2                                                                                                      /                                                    2                                                                                                                                                        2                                                                                                       
(-- + ------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------, -- +       /    - --- + 2*3 /   --------- + --------------  - ---------------------------------------  + |-- + ------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|  +            /    - --- - 2*3 /   --------- + --------------  + --------------------------------------------------------------------------------------------------- + ---------------------------------------  + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------)
 20                                                   2                                                                                                                                                        2                                                                                                        10        /       300     \/    216000000      1080000                   ____________________________    \20                                                   2                                                                                                                                                        2                                                                                                      /              /       150     \/    216000000      1080000                    _______________________________________________________________________________________              ____________________________                                                                                                                                                                                                                                                                                          _____________________________________________________________________________________________________________________________________________________________________________________________                                                                                                                                                              
                                                                                                                                                                                                                                                                                                                                 /                                                              /               ____________                                                                                                                                                                                                                                                                                                                                         /                                                               /                ____________________________                                                        /               ____________                                                                                                                                                                                                                                                                                          /                ____________________________                                                                                                                                                                                                                                                                                                               
                                                                                                                                                                                                                                                                                                                                /                                                              /   8313701    \/ 1799507686                                                                                                                                                                                                                                                                                                                                         /                                                               /                /               ____________                                                        /   8313701    \/ 1799507686                                                                                                                                                                                                                                                                                          /                /               ____________                                                                                                                                                                                                                                                                                                                
                                                                                                                                                                                                                                                                                                                               /                                                      60000*3 /   --------- + --------------                                                                                                                                                                                                                                                                                                                                       /                                                               /     199        /   8313701    \/ 1799507686                       4733                     60000*3 /   --------- + --------------                                                                                                                                                                                                                                                                                        /     199        /   8313701    \/ 1799507686                                                      1                                                                      4733                                                                                                                                                                                
                                                                                                                                                                                                                                                                                                                             \/                                                             \/    216000000      1080000                                                                                                                                                                                                                                                                                                                                          /                                                       5*      /    - --- + 2*3 /   --------- + --------------  - ---------------------------------------          \/    216000000      1080000                                                                                                                                                                                                                                                                                           /    - --- - 2*3 /   --------- + --------------  + --------------------------------------------------------------------------------------------------- + ---------------------------------------                                                                                                                                                               
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 /                                                               /       300     \/    216000000      1080000                   ____________________________                                                                                                                                                                                                                            _______________________________________________________________________________________             /       150     \/    216000000      1080000                    _______________________________________________________________________________________              ____________________________                                                                                                                                                               
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                /                                                               /                                                              /               ____________                                                                                                                                                                                                                            /                ____________________________                                                       /                                                               /                ____________________________                                                        /               ____________                                                                                                                                                                
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               /                                                               /                                                              /   8313701    \/ 1799507686                                                                                                                                                                                                                            /                /               ____________                                                       /                                                               /                /               ____________                                                        /   8313701    \/ 1799507686                                                                                                                                                                 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              /                                                               /                                                      60000*3 /   --------- + --------------                                                                                                                                                                                                                          /     199        /   8313701    \/ 1799507686                       4733                            /                                                               /     199        /   8313701    \/ 1799507686                       4733                     60000*3 /   --------- + --------------                                                                                                                                                                
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            \/                                                              \/                                                             \/    216000000      1080000                                                                                                                                                                                                                             /    - --- + 2*3 /   --------- + --------------  - ---------------------------------------          /                                                       5*      /    - --- + 2*3 /   --------- + --------------  - ---------------------------------------          \/    216000000      1080000                                                                                                                                                                    
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   /       300     \/    216000000      1080000                   ____________________________         /                                                               /       300     \/    216000000      1080000                   ____________________________                                                                                                                                                                                                          
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  /                                                              /               ____________         /                                                               /                                                              /               ____________                                                                                                                                                                                                           
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 /                                                              /   8313701    \/ 1799507686         /                                                               /                                                              /   8313701    \/ 1799507686                                                                                                                                                                                                            
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                /                                                      60000*3 /   --------- + --------------       /                                                               /                                                      60000*3 /   --------- + --------------                                                                                                                                                                                                           
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         1    \/                                                             \/    216000000      1080000         \/                                                              \/                                                             \/    216000000      1080000                                                                                                                                                                                                               
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       - -- + ------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------                                                                                                                                                              
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         20                                                   2                                                                                                                                                        2

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       2                                                                                                                                                                                                                                                                                                                    
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                /                                                                                                                        _____________________________________________________________________________________________________________________________________________________________________________________________\                                                                                                                       _____________________________________________________________________________________________________________________________________________________________________________________________ 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        3                                                                                                                                                                                                                       |                                                                                                                       /                ____________________________                                                                                                                                                 |                                                                                                                      /                ____________________________                                                                                                                                                  
                                                                                                                         _____________________________________________________________________________________________________________________________________________________________________________________________                                                                                                           /                                                                                                                        _____________________________________________________________________________________________________________________________________________________________________________________________\                                                                                                                                                                                                                        |                                                                                                                      /                /               ____________                                                                                                                                                  |                                                                                                                     /                /               ____________                                                                                                                                                   
                                                                                                                        /                ____________________________                                                                                                                                                                                                                                                            |                                                                                                                       /                ____________________________                                                                                                                                                 |                                                                                                                                                                                                                        |                                                                                                                     /     199        /   8313701    \/ 1799507686                                                      1                                                                      4733                  |                                                                                                                    /     199        /   8313701    \/ 1799507686                                                      1                                                                      4733                   
                                                                                                                       /                /               ____________                                                                                                                                                                                                                                                             |                                                                                                                      /                /               ____________                                                                                                                                                  |                                                                                                                                                                                                                        |                                                                                                                    /    - --- - 2*3 /   --------- + --------------  + --------------------------------------------------------------------------------------------------- + --------------------------------------- |                                                                                                                   /    - --- - 2*3 /   --------- + --------------  + --------------------------------------------------------------------------------------------------- + ---------------------------------------  
                                                                                                                      /     199        /   8313701    \/ 1799507686                                                      1                                                                      4733                                                                                                                             |                                                                                                                     /     199        /   8313701    \/ 1799507686                                                      1                                                                      4733                  |                                                                                                                                                                                                                        |               _______________________________________________________________________________________             /       150     \/    216000000      1080000                    _______________________________________________________________________________________              ____________________________ |              _______________________________________________________________________________________             /       150     \/    216000000      1080000                    _______________________________________________________________________________________              ____________________________  
                                                                                                                     /    - --- - 2*3 /   --------- + --------------  + --------------------------------------------------------------------------------------------------- + ---------------------------------------                                                                                                            |                                                                                                                    /    - --- - 2*3 /   --------- + --------------  + --------------------------------------------------------------------------------------------------- + --------------------------------------- |                                                                                                                                                                                                                        |              /                ____________________________                                                       /                                                               /                ____________________________                                                        /               ____________  |             /                ____________________________                                                       /                                                               /                ____________________________                                                        /               ____________   
                _______________________________________________________________________________________             /       150     \/    216000000      1080000                    _______________________________________________________________________________________              ____________________________                                                                                                            |               _______________________________________________________________________________________             /       150     \/    216000000      1080000                    _______________________________________________________________________________________              ____________________________ |                                                                                                                                                                                                                        |             /                /               ____________                                                       /                                                               /                /               ____________                                                        /   8313701    \/ 1799507686   |            /                /               ____________                                                       /                                                               /                /               ____________                                                        /   8313701    \/ 1799507686    
               /                ____________________________                                                       /                                                               /                ____________________________                                                        /               ____________                                                                                                             |              /                ____________________________                                                       /                                                               /                ____________________________                                                        /               ____________  |                                                                                                                                                                                                                        |            /     199        /   8313701    \/ 1799507686                       4733                            /                                                               /     199        /   8313701    \/ 1799507686                       4733                     60000*3 /   --------- + --------------  |           /     199        /   8313701    \/ 1799507686                       4733                            /                                                               /     199        /   8313701    \/ 1799507686                       4733                     60000*3 /   --------- + --------------   
              /                /               ____________                                                       /                                                               /                /               ____________                                                        /   8313701    \/ 1799507686                                                                                                              |             /                /               ____________                                                       /                                                               /                /               ____________                                                        /   8313701    \/ 1799507686   |                                                                                                                                                                                                                        |           /    - --- + 2*3 /   --------- + --------------  - ---------------------------------------          /                                                       5*      /    - --- + 2*3 /   --------- + --------------  - ---------------------------------------          \/    216000000      1080000      |          /    - --- + 2*3 /   --------- + --------------  - ---------------------------------------          /                                                       5*      /    - --- + 2*3 /   --------- + --------------  - ---------------------------------------          \/    216000000      1080000       
             /     199        /   8313701    \/ 1799507686                       4733                            /                                                               /     199        /   8313701    \/ 1799507686                       4733                     60000*3 /   --------- + --------------                                                                                                             |            /     199        /   8313701    \/ 1799507686                       4733                            /                                                               /     199        /   8313701    \/ 1799507686                       4733                     60000*3 /   --------- + --------------  |                                                                                                                                                                                                                        |          /       300     \/    216000000      1080000                   ____________________________         /                                                               /       300     \/    216000000      1080000                   ____________________________                                            |         /       300     \/    216000000      1080000                   ____________________________         /                                                               /       300     \/    216000000      1080000                   ____________________________                                             
            /    - --- + 2*3 /   --------- + --------------  - ---------------------------------------          /                                                       5*      /    - --- + 2*3 /   --------- + --------------  - ---------------------------------------          \/    216000000      1080000                                                                                                                 |           /    - --- + 2*3 /   --------- + --------------  - ---------------------------------------          /                                                       5*      /    - --- + 2*3 /   --------- + --------------  - ---------------------------------------          \/    216000000      1080000      |                                                                                                                                                                                                                        |         /                                                              /               ____________         /                                                               /                                                              /               ____________                                             |        /                                                              /               ____________         /                                                               /                                                              /               ____________                                              
           /       300     \/    216000000      1080000                   ____________________________         /                                                               /       300     \/    216000000      1080000                   ____________________________                                                                                                                                                       |          /       300     \/    216000000      1080000                   ____________________________         /                                                               /       300     \/    216000000      1080000                   ____________________________                                            |                                                                                                                                                                                                                        |        /                                                              /   8313701    \/ 1799507686         /                                                               /                                                              /   8313701    \/ 1799507686                                              |       /                                                              /   8313701    \/ 1799507686         /                                                               /                                                              /   8313701    \/ 1799507686                                               
          /                                                              /               ____________         /                                                               /                                                              /               ____________                                                              _______________________________________________________________________________________   |         /                                                              /               ____________         /                                                               /                                                              /               ____________                                             |                   _____________________________________________________________________________________________________________________________________________________________________________________________        |       /                                                      60000*3 /   --------- + --------------       /                                                               /                                                      60000*3 /   --------- + --------------                                             |      /                                                      60000*3 /   --------- + --------------       /                                                               /                                                      60000*3 /   --------- + --------------                                              
         /                                                              /   8313701    \/ 1799507686         /                                                               /                                                              /   8313701    \/ 1799507686                                                              /                ____________________________                                              |        /                                                              /   8313701    \/ 1799507686         /                                                               /                                                              /   8313701    \/ 1799507686                                              |                  /                ____________________________                                                                                                                                                    11   |1    \/                                                             \/    216000000      1080000         \/                                                              \/                                                             \/    216000000      1080000                                                 |    \/                                                             \/    216000000      1080000         \/                                                              \/                                                             \/    216000000      1080000                                                  
        /                                                      60000*3 /   --------- + --------------       /                                                               /                                                      60000*3 /   --------- + --------------                                                            /                /               ____________                                               |       /                                                      60000*3 /   --------- + --------------       /                                                               /                                                      60000*3 /   --------- + --------------                                             |                 /                /               ____________                                                                                                                                                     -- + |-- + ------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|  + ------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 
 1    \/                                                             \/    216000000      1080000         \/                                                              \/                                                             \/    216000000      1080000                                                   1           /     199        /   8313701    \/ 1799507686                       4733                     |1    \/                                                             \/    216000000      1080000         \/                                                              \/                                                             \/    216000000      1080000                                                 |                /     199        /   8313701    \/ 1799507686                                                      1                                                                      4733                     20   \20                                                   2                                                                                                                                                        2                                                                                                      /                                                    2                                                                                                                                                        2                                                                                                       
(-- + ------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------, -- +       /    - --- + 2*3 /   --------- + --------------  - ---------------------------------------  + |-- + ------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|  -            /    - --- - 2*3 /   --------- + --------------  + --------------------------------------------------------------------------------------------------- + ---------------------------------------  + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------)
 20                                                   2                                                                                                                                                        2                                                                                                        10        /       300     \/    216000000      1080000                   ____________________________    \20                                                   2                                                                                                                                                        2                                                                                                      /              /       150     \/    216000000      1080000                    _______________________________________________________________________________________              ____________________________                                                                                                                                                                                                                                                                                          _____________________________________________________________________________________________________________________________________________________________________________________________                                                                                                                                                              
                                                                                                                                                                                                                                                                                                                                 /                                                              /               ____________                                                                                                                                                                                                                                                                                                                                         /                                                               /                ____________________________                                                        /               ____________                                                                                                                                                                                                                                                                                          /                ____________________________                                                                                                                                                                                                                                                                                                               
                                                                                                                                                                                                                                                                                                                                /                                                              /   8313701    \/ 1799507686                                                                                                                                                                                                                                                                                                                                         /                                                               /                /               ____________                                                        /   8313701    \/ 1799507686                                                                                                                                                                                                                                                                                          /                /               ____________                                                                                                                                                                                                                                                                                                                
                                                                                                                                                                                                                                                                                                                               /                                                      60000*3 /   --------- + --------------                                                                                                                                                                                                                                                                                                                                       /                                                               /     199        /   8313701    \/ 1799507686                       4733                     60000*3 /   --------- + --------------                                                                                                                                                                                                                                                                                        /     199        /   8313701    \/ 1799507686                                                      1                                                                      4733                                                                                                                                                                                
                                                                                                                                                                                                                                                                                                                             \/                                                             \/    216000000      1080000                                                                                                                                                                                                                                                                                                                                          /                                                       5*      /    - --- + 2*3 /   --------- + --------------  - ---------------------------------------          \/    216000000      1080000                                                                                                                                                                                                                                                                                           /    - --- - 2*3 /   --------- + --------------  + --------------------------------------------------------------------------------------------------- + ---------------------------------------                                                                                                                                                               
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 /                                                               /       300     \/    216000000      1080000                   ____________________________                                                                                                                                                                                                                            _______________________________________________________________________________________             /       150     \/    216000000      1080000                    _______________________________________________________________________________________              ____________________________                                                                                                                                                               
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                /                                                               /                                                              /               ____________                                                                                                                                                                                                                            /                ____________________________                                                       /                                                               /                ____________________________                                                        /               ____________                                                                                                                                                                
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               /                                                               /                                                              /   8313701    \/ 1799507686                                                                                                                                                                                                                            /                /               ____________                                                       /                                                               /                /               ____________                                                        /   8313701    \/ 1799507686                                                                                                                                                                 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              /                                                               /                                                      60000*3 /   --------- + --------------                                                                                                                                                                                                                          /     199        /   8313701    \/ 1799507686                       4733                            /                                                               /     199        /   8313701    \/ 1799507686                       4733                     60000*3 /   --------- + --------------                                                                                                                                                                
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            \/                                                              \/                                                             \/    216000000      1080000                                                                                                                                                                                                                             /    - --- + 2*3 /   --------- + --------------  - ---------------------------------------          /                                                       5*      /    - --- + 2*3 /   --------- + --------------  - ---------------------------------------          \/    216000000      1080000                                                                                                                                                                    
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   /       300     \/    216000000      1080000                   ____________________________         /                                                               /       300     \/    216000000      1080000                   ____________________________                                                                                                                                                                                                          
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  /                                                              /               ____________         /                                                               /                                                              /               ____________                                                                                                                                                                                                           
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 /                                                              /   8313701    \/ 1799507686         /                                                               /                                                              /   8313701    \/ 1799507686                                                                                                                                                                                                            
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                /                                                      60000*3 /   --------- + --------------       /                                                               /                                                      60000*3 /   --------- + --------------                                                                                                                                                                                                           
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         1    \/                                                             \/    216000000      1080000         \/                                                              \/                                                             \/    216000000      1080000                                                                                                                                                                                                               
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       - -- + ------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------                                                                                                                                                              
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         20                                                   2                                                                                                                                                        2

Intervalos de crecimiento y decrecimiento de la función:
Hallemos los intervalos donde la función crece y decrece y también los puntos mínimos y máximos de la función, para lo cual miramos cómo se comporta la función en los extremos con desviación mínima del extremo:
Puntos mínimos de la función:

x_{1} = \frac{\sqrt{- \frac{199}{300} - \frac{4733}{60000 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}} + 2 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}}}{2} + \frac{1}{20} + \frac{\sqrt{\left|{- \frac{199}{150} - 2 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}} + \frac{4733}{60000 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}} + \frac{1}{5 \sqrt{- \frac{199}{300} - \frac{4733}{60000 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}} + 2 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}}}}\right|}}{2}

Puntos máximos de la función:

x_{1} = - \frac{\sqrt{\left|{- \frac{199}{150} - 2 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}} + \frac{4733}{60000 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}} + \frac{1}{5 \sqrt{- \frac{199}{300} - \frac{4733}{60000 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}} + 2 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}}}}\right|}}{2} + \frac{\sqrt{- \frac{199}{300} - \frac{4733}{60000 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}} + 2 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}}}{2} + \frac{1}{20}

Decrece en los intervalos

\left(-\infty, - \frac{\sqrt{\left|{- \frac{199}{150} - 2 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}} + \frac{4733}{60000 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}} + \frac{1}{5 \sqrt{- \frac{199}{300} - \frac{4733}{60000 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}} + 2 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}}}}\right|}}{2} + \frac{\sqrt{- \frac{199}{300} - \frac{4733}{60000 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}} + 2 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}}}{2} + \frac{1}{20}\right] \cup \left[\frac{\sqrt{- \frac{199}{300} - \frac{4733}{60000 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}} + 2 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}}}{2} + \frac{1}{20} + \frac{\sqrt{\left|{- \frac{199}{150} - 2 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}} + \frac{4733}{60000 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}} + \frac{1}{5 \sqrt{- \frac{199}{300} - \frac{4733}{60000 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}} + 2 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}}}}\right|}}{2}, \infty\right)

Crece en los intervalos

\left[- \frac{\sqrt{\left|{- \frac{199}{150} - 2 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}} + \frac{4733}{60000 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}} + \frac{1}{5 \sqrt{- \frac{199}{300} - \frac{4733}{60000 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}} + 2 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}}}}\right|}}{2} + \frac{\sqrt{- \frac{199}{300} - \frac{4733}{60000 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}} + 2 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}}}{2} + \frac{1}{20}, \frac{\sqrt{- \frac{199}{300} - \frac{4733}{60000 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}} + 2 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}}}{2} + \frac{1}{20} + \frac{\sqrt{\left|{- \frac{199}{150} - 2 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}} + \frac{4733}{60000 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}} + \frac{1}{5 \sqrt{- \frac{199}{300} - \frac{4733}{60000 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}} + 2 \sqrt[3]{\frac{8313701}{216000000} + \frac{\sqrt{1799507686}}{1080000}}}}}\right|}}{2}\right]

Puntos de flexiones

Hallemos los puntos de flexiones, para eso hay que resolver la ecuación

\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0

(la segunda derivada es igual a cero),
las raíces de la ecuación obtenida serán los puntos de flexión para el gráfico de la función indicado:

\frac{d^{2}}{d x^{2}} f{\left(x \right)} =

segunda derivada

2 \left(3 x - \frac{100 \left(2 x + 1\right)}{\left(10 x - 1\right)^{2}} + \frac{10}{10 x - 1} + \frac{500 \left(2 x^{2} + 2 x + 1\right)}{\left(10 x - 1\right)^{3}}\right) = 0

Resolvermos esta ecuación
Soluciones no halladas,
tal vez la función no tenga flexiones

Asíntotas verticales

Hay:

x_{1} = 0.1

Asíntotas horizontales

Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo

\lim_{x \to -\infty}\left(\left(x^{3} + 2 x\right) + \frac{\left(x^{2} + x\right) + \frac{1}{2}}{x - \frac{1}{10}}\right) = -\infty

Tomamos como el límite
es decir,
no hay asíntota horizontal a la izquierda

\lim_{x \to \infty}\left(\left(x^{3} + 2 x\right) + \frac{\left(x^{2} + x\right) + \frac{1}{2}}{x - \frac{1}{10}}\right) = \infty

Tomamos como el límite
es decir,
no hay asíntota horizontal a la derecha

Asíntotas inclinadas

Se puede hallar la asíntota inclinada calculando el límite de la función x^3 + 2*x + (x^2 + x + 1/2)/(x - 1/10), dividida por x con x->+oo y x ->-oo

\lim_{x \to -\infty}\left(\frac{\left(x^{3} + 2 x\right) + \frac{\left(x^{2} + x\right) + \frac{1}{2}}{x - \frac{1}{10}}}{x}\right) = \infty

Tomamos como el límite
es decir,
no hay asíntota inclinada a la izquierda

\lim_{x \to \infty}\left(\frac{\left(x^{3} + 2 x\right) + \frac{\left(x^{2} + x\right) + \frac{1}{2}}{x - \frac{1}{10}}}{x}\right) = \infty

Tomamos como el límite
es decir,
no hay asíntota inclinada a la derecha

Paridad e imparidad de la función

Comprobemos si la función es par o impar mediante las relaciones f = f(-x) и f = -f(-x).
Pues, comprobamos:

\left(x^{3} + 2 x\right) + \frac{\left(x^{2} + x\right) + \frac{1}{2}}{x - \frac{1}{10}} = - x^{3} - 2 x + \frac{x^{2} - x + \frac{1}{2}}{- x - \frac{1}{10}}

- No

\left(x^{3} + 2 x\right) + \frac{\left(x^{2} + x\right) + \frac{1}{2}}{x - \frac{1}{10}} = x^{3} + 2 x - \frac{x^{2} - x + \frac{1}{2}}{- x - \frac{1}{10}}

- No
es decir, función
no es
par ni impar

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Gráfico de la función y = x^3+2x+1/(x-(1/10))(x^2+x+(1/2))

Gráfico:

Puntos de intersección:

Definida a trozos:

Solución

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Gráfico de la función y = x^3+2*x+1/(x-(1/10))*(x^2+x+(1/2))

Gráfico:

Puntos de intersección:

Definida a trozos:

Solución

Gráfico de la función y = x^3+2x+1/(x-(1/10))(x^2+x+(1/2))