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Otras calculadoras
- Gráfico de la función implícita
- Derivadas paso a paso
- Integrales paso a paso
- Gráfico de la función paramétrica
- Gráfico en coordenadas polares
- Superficie especificada paramétricamente
- Superficie dada por la ecuación
- Curva en el espacio especificada paramétricamente
- Superficie de una figura limitada con líneas
- Puntos de cruce de las funciones
-
¿Cómo usar?
- Gráfico de la función y =:
-
x-x^3
-
x^4-2x^2
-
1-x^3
-
x^2/(x-3)
-
Expresiones idénticas
- abs(x-(uno /x^ dos))-cos(x)/(log(abs(tan(x)-x)))* dos *x^ dos + seis *x+ nueve
- abs(x menos (1 dividir por x al cuadrado )) menos coseno de (x) dividir por ( logaritmo de (abs( tangente de (x) menos x))) multiplicar por 2 multiplicar por x al cuadrado más 6 multiplicar por x más 9
- abs(x menos (uno dividir por x en el grado dos)) menos coseno de (x) dividir por ( logaritmo de (abs( tangente de (x) menos x))) multiplicar por dos multiplicar por x en el grado dos más seis multiplicar por x más nueve
- abs(x-(1/x2))-cos(x)/(log(abs(tan(x)-x)))*2*x2+6*x+9
- absx-1/x2-cosx/logabstanx-x*2*x2+6*x+9
- abs(x-(1/x²))-cos(x)/(log(abs(tan(x)-x)))*2*x²+6*x+9
- abs(x-(1/x en el grado 2))-cos(x)/(log(abs(tan(x)-x)))*2*x en el grado 2+6*x+9
- abs(x-(1/x^2))-cos(x)/(log(abs(tan(x)-x)))2x^2+6x+9
- abs(x-(1/x2))-cos(x)/(log(abs(tan(x)-x)))2x2+6x+9
- absx-1/x2-cosx/logabstanx-x2x2+6x+9
- absx-1/x^2-cosx/logabstanx-x2x^2+6x+9
- abs(x-(1 dividir por x^2))-cos(x) dividir por (log(abs(tan(x)-x)))*2*x^2+6*x+9
-
Expresiones semejantes
- abs(x+(1/x^2))-cos(x)/(log(abs(tan(x)-x)))*2*x^2+6*x+9
- abs(x-(1/x^2))+cos(x)/(log(abs(tan(x)-x)))*2*x^2+6*x+9
- abs(x-(1/x^2))-cos(x)/(log(abs(tan(x)-x)))*2*x^2-6*x+9
- abs(x-(1/x^2))-cos(x)/(log(abs(tan(x)-x)))*2*x^2+6*x-9
- abs(x-(1/x^2))-cos(x)/(log(abs(tan(x)+x)))*2*x^2+6*x+9
- abs(x-(1/x^2))-cosx/(log(abs(tan(x)-x)))*2*x^2+6*x+9
-
Expresiones con funciones
- abs
- abs(2x)
- absolute(3x+1)
- abs(tan(y)*0.0015+0.5)
- absolute(x^2-3x+2)+2x-3
- absolute(x)+cos(x)
- Coseno cos
- cos^2(x)-cos(x)
- cos(x)/x
- cos(0.5x)-1
- cosx-x
- cos(x)*2
- Logaritmo log
- log(10*x)
- log(x)*cos(x)^(2)
- log(x/(x+1))
- logx4
- log(4*x+5)
- abs
- abs(2x)
- absolute(3x+1)
- abs(tan(y)*0.0015+0.5)
- absolute(x^2-3x+2)+2x-3
- absolute(x)+cos(x)
- Tangente tan
- tan(3*x)
- tan(x)*sin(x)
- tan(x)^(3)
- tan(x+pi/4)
- tan(x)/((3*x))
Gráfico de la función y = abs(x-(1/x^2))-cos(x)/(log(abs(tan(x)-x)))*2*x^2+6*x+9
Solución
Ha introducido
[src]
| 1 | cos(x) 2
f(x) = |x - --| - -----------------*2*x + 6*x + 9
| 2| log(|tan(x) - x|)
| x |
$$f{\left(x \right)} = \left(6 x + \left(- x^{2} \cdot 2 \frac{\cos{\left(x \right)}}{\log{\left(\left|{- x + \tan{\left(x \right)}}\right| \right)}} + \left|{x - \frac{1}{x^{2}}}\right|\right)\right) + 9$$
f = 6*x - x^2*2*(cos(x)/log(Abs(-x + tan(x)))) + |x - 1/x^2| + 9
Gráfico de la función
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:
$$\left(6 x + \left(- x^{2} \cdot 2 \frac{\cos{\left(x \right)}}{\log{\left(\left|{- x + \tan{\left(x \right)}}\right| \right)}} + \left|{x - \frac{1}{x^{2}}}\right|\right)\right) + 9 = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución numérica
$$x_{1} = -29.5840925099944$$
$$x_{2} = -1.19259845190913$$
$$x_{3} = 89.3585389006903$$
$$x_{4} = -89.6608799353666$$
$$x_{5} = -48.5066339739556$$
$$x_{6} = 83.0648105337411$$
$$x_{7} = 26.2412380070532$$
$$x_{8} = -95.9376849504223$$
$$x_{9} = 57.8703512180766$$
$$x_{10} = -35.8977749044837$$
$$x_{11} = 80.3087756891324$$
$$x_{12} = -64.5636512938857$$
$$x_{13} = -20.7745995057727$$
$$x_{14} = 32.5967018004127$$
$$x_{15} = 55.2452711405908$$
$$x_{16} = -52.0251692380596$$
$$x_{17} = -33.2464760709665$$
$$x_{18} = 92.8532948837997$$
$$x_{19} = -92.5593332340683$$
$$x_{20} = -14.5743503373268$$
$$x_{21} = 24.0829423022591$$
$$x_{22} = -23.2600806167803$$
$$x_{23} = 67.771316219314$$
$$x_{24} = -83.3848774934392$$
$$x_{25} = 11.9611644819678$$
$$x_{26} = -98.848214093588$$
$$x_{27} = 48.9890258533454$$
$$x_{28} = -45.7604285065276$$
$$x_{29} = 36.5006831893491$$
$$x_{30} = 17.9447090419093$$
$$x_{31} = -79.979394577634$$
$$x_{32} = -54.805254115777$$
$$x_{33} = 38.930352049396$$
$$x_{34} = 13.3270262323497$$
$$x_{35} = -39.5002051024911$$
$$x_{36} = 70.4724540846309$$
$$x_{37} = 64.1729512837875$$
$$x_{38} = -16.920366948233$$
$$x_{39} = -67.3954387726728$$
$$x_{40} = -86.2697718477369$$
$$x_{41} = 51.5636123768479$$
$$x_{42} = -8.42091417831353$$
$$x_{43} = -73.688026746585$$
$$x_{44} = 95.6510338829714$$
$$x_{45} = -77.1098460757445$$
$$x_{46} = 61.5064642047667$$
$$x_{47} = -61.1013225001357$$
$$x_{48} = 42.7397293601088$$
$$x_{49} = 86.5803310311679$$
$$x_{50} = -70.836005985521$$
$$x_{51} = -10.5649464554785$$
$$x_{52} = -42.2045850897045$$
$$x_{53} = 19.8427215536707$$
$$x_{54} = -27.0025826467422$$
$$x_{55} = 30.27779658204$$
$$x_{56} = -58.2931839968355$$
$$x_{57} = 45.2511412457967$$
$$x_{58} = 99.1274182279726$$
$$x_{59} = 74.0389568584821$$
$$x_{60} = 76.769572043515$$
o sea hay que resolver la ecuación:
$$\left(6 x + \left(- x^{2} \cdot 2 \frac{\cos{\left(x \right)}}{\log{\left(\left|{- x + \tan{\left(x \right)}}\right| \right)}} + \left|{x - \frac{1}{x^{2}}}\right|\right)\right) + 9 = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución numérica
$$x_{1} = -29.5840925099944$$
$$x_{2} = -1.19259845190913$$
$$x_{3} = 89.3585389006903$$
$$x_{4} = -89.6608799353666$$
$$x_{5} = -48.5066339739556$$
$$x_{6} = 83.0648105337411$$
$$x_{7} = 26.2412380070532$$
$$x_{8} = -95.9376849504223$$
$$x_{9} = 57.8703512180766$$
$$x_{10} = -35.8977749044837$$
$$x_{11} = 80.3087756891324$$
$$x_{12} = -64.5636512938857$$
$$x_{13} = -20.7745995057727$$
$$x_{14} = 32.5967018004127$$
$$x_{15} = 55.2452711405908$$
$$x_{16} = -52.0251692380596$$
$$x_{17} = -33.2464760709665$$
$$x_{18} = 92.8532948837997$$
$$x_{19} = -92.5593332340683$$
$$x_{20} = -14.5743503373268$$
$$x_{21} = 24.0829423022591$$
$$x_{22} = -23.2600806167803$$
$$x_{23} = 67.771316219314$$
$$x_{24} = -83.3848774934392$$
$$x_{25} = 11.9611644819678$$
$$x_{26} = -98.848214093588$$
$$x_{27} = 48.9890258533454$$
$$x_{28} = -45.7604285065276$$
$$x_{29} = 36.5006831893491$$
$$x_{30} = 17.9447090419093$$
$$x_{31} = -79.979394577634$$
$$x_{32} = -54.805254115777$$
$$x_{33} = 38.930352049396$$
$$x_{34} = 13.3270262323497$$
$$x_{35} = -39.5002051024911$$
$$x_{36} = 70.4724540846309$$
$$x_{37} = 64.1729512837875$$
$$x_{38} = -16.920366948233$$
$$x_{39} = -67.3954387726728$$
$$x_{40} = -86.2697718477369$$
$$x_{41} = 51.5636123768479$$
$$x_{42} = -8.42091417831353$$
$$x_{43} = -73.688026746585$$
$$x_{44} = 95.6510338829714$$
$$x_{45} = -77.1098460757445$$
$$x_{46} = 61.5064642047667$$
$$x_{47} = -61.1013225001357$$
$$x_{48} = 42.7397293601088$$
$$x_{49} = 86.5803310311679$$
$$x_{50} = -70.836005985521$$
$$x_{51} = -10.5649464554785$$
$$x_{52} = -42.2045850897045$$
$$x_{53} = 19.8427215536707$$
$$x_{54} = -27.0025826467422$$
$$x_{55} = 30.27779658204$$
$$x_{56} = -58.2931839968355$$
$$x_{57} = 45.2511412457967$$
$$x_{58} = 99.1274182279726$$
$$x_{59} = 74.0389568584821$$
$$x_{60} = 76.769572043515$$
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
$$x^{2} \left(\frac{2 \sin{\left(x \right)}}{\log{\left(\left|{- x + \tan{\left(x \right)}}\right| \right)}} + \frac{2 \cos{\left(x \right)} \tan^{2}{\left(x \right)} \operatorname{sign}{\left(- x + \tan{\left(x \right)} \right)}}{\log{\left(\left|{- x + \tan{\left(x \right)}}\right| \right)}^{2} \left|{- x + \tan{\left(x \right)}}\right|}\right) - \frac{4 x \cos{\left(x \right)}}{\log{\left(\left|{- x + \tan{\left(x \right)}}\right| \right)}} + \left(1 + \frac{2}{x^{3}}\right) \operatorname{sign}{\left(x - \frac{1}{x^{2}} \right)} + 6 = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = 18.9264058354201$$
$$x_{2} = 50.2998142615969$$
$$x_{3} = -53.4410077699145$$
$$x_{4} = -12.7614185116853$$
$$x_{5} = 44.0208807826813$$
$$x_{6} = 72.2871602270437$$
$$x_{7} = 100.549257995514$$
$$x_{8} = -81.7075317813637$$
$$x_{9} = -75.4266346827908$$
$$x_{10} = -59.7208761622848$$
$$x_{11} = -37.758412241665$$
$$x_{12} = -66.001338580364$$
$$x_{13} = 40.8973432278724$$
$$x_{14} = -72.2822481243589$$
$$x_{15} = -106.833892440804$$
$$x_{16} = 69.1408591269651$$
$$x_{17} = -87.9887673331621$$
$$x_{18} = 78.5677422051829$$
$$x_{19} = -44.0325759301551$$
$$x_{20} = -78.563502726215$$
$$x_{21} = -6.68642743061798$$
$$x_{22} = -100.551993225384$$
$$x_{23} = 97.4115904152189$$
$$x_{24} = -40.884054909174$$
$$x_{25} = -15.8067010908366$$
$$x_{26} = -91.1267738597789$$
$$x_{27} = 25.1942813811105$$
$$x_{28} = -25.2245963745014$$
$$x_{29} = 15.871906339153$$
$$x_{30} = -3.4855577220419$$
$$x_{31} = 59.7277486157697$$
$$x_{32} = 56.5795967393325$$
$$x_{33} = -69.1461717480462$$
$$x_{34} = 81.7035764585142$$
$$x_{35} = -9.57178791799043$$
$$x_{36} = -47.1619528823701$$
$$x_{37} = 75.4220778711379$$
$$x_{38} = 53.4493547996909$$
$$x_{39} = -84.8450292391343$$
$$x_{40} = 9.71336796192775$$
$$x_{41} = 94.2672035142578$$
$$x_{42} = 12.6687201304769$$
$$x_{43} = -1.77810988385759$$
$$x_{44} = 22.1036243063686$$
$$x_{45} = 62.8599964822152$$
$$x_{46} = -94.2702717458136$$
$$x_{47} = 34.6255785634057$$
$$x_{48} = -22.0658159146584$$
$$x_{49} = 47.172329623982$$
$$x_{50} = 6.43748560224016$$
$$x_{51} = -34.6078835525902$$
$$x_{52} = -31.4880803517962$$
$$x_{53} = 91.1300326089527$$
$$x_{54} = 87.9852989815678$$
$$x_{55} = -56.5871516552196$$
$$x_{56} = -18.9751325961568$$
$$x_{57} = -62.8662782477935$$
$$x_{58} = 37.7431608214804$$
$$x_{59} = -50.3090917332535$$
$$x_{60} = 28.3593255982933$$
$$x_{61} = 84.8487286205416$$
$$x_{62} = -28.3344594475311$$
$$x_{63} = -97.408696123488$$
$$x_{64} = 0.672717116300184$$
$$x_{65} = 66.0071040861331$$
$$x_{66} = 31.4672625504045$$
Signos de extremos en los puntos:
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:
$$x_{1} = 18.9264058354201$$
$$x_{2} = 50.2998142615969$$
$$x_{3} = -12.7614185116853$$
$$x_{4} = 44.0208807826813$$
$$x_{5} = 100.549257995514$$
$$x_{6} = -81.7075317813637$$
$$x_{7} = -75.4266346827908$$
$$x_{8} = -37.758412241665$$
$$x_{9} = -106.833892440804$$
$$x_{10} = 69.1408591269651$$
$$x_{11} = -87.9887673331621$$
$$x_{12} = -44.0325759301551$$
$$x_{13} = -6.68642743061798$$
$$x_{14} = -100.551993225384$$
$$x_{15} = 25.1942813811105$$
$$x_{16} = -25.2245963745014$$
$$x_{17} = 56.5795967393325$$
$$x_{18} = -69.1461717480462$$
$$x_{19} = 81.7035764585142$$
$$x_{20} = 75.4220778711379$$
$$x_{21} = 94.2672035142578$$
$$x_{22} = 12.6687201304769$$
$$x_{23} = -1.77810988385759$$
$$x_{24} = 62.8599964822152$$
$$x_{25} = -94.2702717458136$$
$$x_{26} = 6.43748560224016$$
$$x_{27} = -31.4880803517962$$
$$x_{28} = 87.9852989815678$$
$$x_{29} = -56.5871516552196$$
$$x_{30} = -18.9751325961568$$
$$x_{31} = -62.8662782477935$$
$$x_{32} = 37.7431608214804$$
$$x_{33} = -50.3090917332535$$
$$x_{34} = 0.672717116300184$$
$$x_{35} = 31.4672625504045$$
Puntos máximos de la función:
$$x_{35} = -53.4410077699145$$
$$x_{35} = 72.2871602270437$$
$$x_{35} = -59.7208761622848$$
$$x_{35} = -66.001338580364$$
$$x_{35} = 40.8973432278724$$
$$x_{35} = -72.2822481243589$$
$$x_{35} = 78.5677422051829$$
$$x_{35} = -78.563502726215$$
$$x_{35} = 97.4115904152189$$
$$x_{35} = -40.884054909174$$
$$x_{35} = -15.8067010908366$$
$$x_{35} = -91.1267738597789$$
$$x_{35} = 15.871906339153$$
$$x_{35} = -3.4855577220419$$
$$x_{35} = 59.7277486157697$$
$$x_{35} = -9.57178791799043$$
$$x_{35} = -47.1619528823701$$
$$x_{35} = 53.4493547996909$$
$$x_{35} = -84.8450292391343$$
$$x_{35} = 9.71336796192775$$
$$x_{35} = 22.1036243063686$$
$$x_{35} = 34.6255785634057$$
$$x_{35} = -22.0658159146584$$
$$x_{35} = 47.172329623982$$
$$x_{35} = -34.6078835525902$$
$$x_{35} = 91.1300326089527$$
$$x_{35} = 28.3593255982933$$
$$x_{35} = 84.8487286205416$$
$$x_{35} = -28.3344594475311$$
$$x_{35} = -97.408696123488$$
$$x_{35} = 66.0071040861331$$
Decrece en los intervalos
$$\left[100.549257995514, \infty\right)$$
Crece en los intervalos
$$\left(-\infty, -106.833892440804\right]$$
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(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
$$x^{2} \left(\frac{2 \sin{\left(x \right)}}{\log{\left(\left|{- x + \tan{\left(x \right)}}\right| \right)}} + \frac{2 \cos{\left(x \right)} \tan^{2}{\left(x \right)} \operatorname{sign}{\left(- x + \tan{\left(x \right)} \right)}}{\log{\left(\left|{- x + \tan{\left(x \right)}}\right| \right)}^{2} \left|{- x + \tan{\left(x \right)}}\right|}\right) - \frac{4 x \cos{\left(x \right)}}{\log{\left(\left|{- x + \tan{\left(x \right)}}\right| \right)}} + \left(1 + \frac{2}{x^{3}}\right) \operatorname{sign}{\left(x - \frac{1}{x^{2}} \right)} + 6 = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = 18.9264058354201$$
$$x_{2} = 50.2998142615969$$
$$x_{3} = -53.4410077699145$$
$$x_{4} = -12.7614185116853$$
$$x_{5} = 44.0208807826813$$
$$x_{6} = 72.2871602270437$$
$$x_{7} = 100.549257995514$$
$$x_{8} = -81.7075317813637$$
$$x_{9} = -75.4266346827908$$
$$x_{10} = -59.7208761622848$$
$$x_{11} = -37.758412241665$$
$$x_{12} = -66.001338580364$$
$$x_{13} = 40.8973432278724$$
$$x_{14} = -72.2822481243589$$
$$x_{15} = -106.833892440804$$
$$x_{16} = 69.1408591269651$$
$$x_{17} = -87.9887673331621$$
$$x_{18} = 78.5677422051829$$
$$x_{19} = -44.0325759301551$$
$$x_{20} = -78.563502726215$$
$$x_{21} = -6.68642743061798$$
$$x_{22} = -100.551993225384$$
$$x_{23} = 97.4115904152189$$
$$x_{24} = -40.884054909174$$
$$x_{25} = -15.8067010908366$$
$$x_{26} = -91.1267738597789$$
$$x_{27} = 25.1942813811105$$
$$x_{28} = -25.2245963745014$$
$$x_{29} = 15.871906339153$$
$$x_{30} = -3.4855577220419$$
$$x_{31} = 59.7277486157697$$
$$x_{32} = 56.5795967393325$$
$$x_{33} = -69.1461717480462$$
$$x_{34} = 81.7035764585142$$
$$x_{35} = -9.57178791799043$$
$$x_{36} = -47.1619528823701$$
$$x_{37} = 75.4220778711379$$
$$x_{38} = 53.4493547996909$$
$$x_{39} = -84.8450292391343$$
$$x_{40} = 9.71336796192775$$
$$x_{41} = 94.2672035142578$$
$$x_{42} = 12.6687201304769$$
$$x_{43} = -1.77810988385759$$
$$x_{44} = 22.1036243063686$$
$$x_{45} = 62.8599964822152$$
$$x_{46} = -94.2702717458136$$
$$x_{47} = 34.6255785634057$$
$$x_{48} = -22.0658159146584$$
$$x_{49} = 47.172329623982$$
$$x_{50} = 6.43748560224016$$
$$x_{51} = -34.6078835525902$$
$$x_{52} = -31.4880803517962$$
$$x_{53} = 91.1300326089527$$
$$x_{54} = 87.9852989815678$$
$$x_{55} = -56.5871516552196$$
$$x_{56} = -18.9751325961568$$
$$x_{57} = -62.8662782477935$$
$$x_{58} = 37.7431608214804$$
$$x_{59} = -50.3090917332535$$
$$x_{60} = 28.3593255982933$$
$$x_{61} = 84.8487286205416$$
$$x_{62} = -28.3344594475311$$
$$x_{63} = -97.408696123488$$
$$x_{64} = 0.672717116300184$$
$$x_{65} = 66.0071040861331$$
$$x_{66} = 31.4672625504045$$
Signos de extremos en los puntos:
(18.92640583542006, -101.769343354913)
(50.299814261596886, -929.876887570917)
(-53.441007769914535, 1176.85724039848)
(-12.761418511685255, -181.056914073388)
(44.020880782681346, -706.376980136213)
(72.28716022704367, 2955.53576436538)
(100.54925799551361, -3672.16202495061)
(-81.70753178136374, -3431.1551358651)
(-75.42663468279082, -2999.25302228719)
(-59.720876162284796, 1453.98336979912)
(-37.75841224166503, -963.997921524853)
(-66.00133858036405, 1757.87635605271)
(40.89734322787239, 1195.58035392363)
(-72.28224812435886, 2088.11969585778)
(-106.83389244080402, -5411.07629160685)
(69.14085912696508, -1763.4456595883)
(-87.98876733316212, -3888.56033769412)
(78.5677422051829, 3387.13213710201)
(-44.032575930155076, -1234.69669950805)
(-78.56350272621502, 2444.34499072505)
(-6.686427430617981, -69.250631480034)
(-100.55199322538377, -4878.7693347274)
(97.41159041521888, 4834.69503681404)
(-40.88405490917401, 704.893146521838)
(-15.806701090836608, 110.523561063908)
(-91.12677385977888, 3233.45578763719)
(25.19428138111053, -207.642321248861)
(-25.224596374501434, -510.152565583937)
(15.871906339152966, 300.588075280485)
(-3.4855577220419027, 11.7169804220918)
(59.727748615769734, 2170.67456051776)
(56.57959673933248, -1180.88577034959)
(-69.1461717480462, -2593.1674279521)
(81.70357645851425, -2450.68878533177)
(-9.571787917990433, 41.9559234841178)
(-47.16195288237008, 926.975186202914)
(75.42207787113792, -2094.1610975484)
(53.4493547996909, 1818.19872013581)
(-84.84502923913432, 2826.22279639294)
(9.713367961927753, 157.651261315906)
(94.26720351425783, -3239.96011571782)
(12.668720130476869, -28.486265328065)
(-1.7781098838575915, 1.1192391859289)
(22.103624306368623, 477.888974648464)
(62.8599964822152, -1458.89025191094)
(-94.27027174581356, -4371.18474257796)
(34.62557856340566, 926.671800233348)
(-22.06581591465841, 212.876223129989)
(47.17232962398199, 1492.97999009949)
(6.437485602240162, 9.47244179660039)
(-34.607883552590195, 511.272666028188)
(-31.48808035179616, -722.173164164373)
(91.13003260895273, 4326.99638602441)
(87.9852989815678, -2832.71619765727)
(-56.58715165521956, -1859.88563961156)
(-18.97513259615679, -329.17342635265)
(-62.86627824779348, -2213.2473964156)
(37.743160821480416, -510.989865039299)
(-50.309091733253545, -1533.52953922317)
(28.3593255982933, 687.0837332611)
(84.8487286205416, 3844.38506630239)
(-28.334459447531096, 346.923439388858)
(-97.40869612348799, 3665.77352805373)
(0.6727171163001838, 14.912374220297)
(66.00710408613314, 2549.92655473021)
(31.46726255040447, -344.44307756174)
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:
$$x_{1} = 18.9264058354201$$
$$x_{2} = 50.2998142615969$$
$$x_{3} = -12.7614185116853$$
$$x_{4} = 44.0208807826813$$
$$x_{5} = 100.549257995514$$
$$x_{6} = -81.7075317813637$$
$$x_{7} = -75.4266346827908$$
$$x_{8} = -37.758412241665$$
$$x_{9} = -106.833892440804$$
$$x_{10} = 69.1408591269651$$
$$x_{11} = -87.9887673331621$$
$$x_{12} = -44.0325759301551$$
$$x_{13} = -6.68642743061798$$
$$x_{14} = -100.551993225384$$
$$x_{15} = 25.1942813811105$$
$$x_{16} = -25.2245963745014$$
$$x_{17} = 56.5795967393325$$
$$x_{18} = -69.1461717480462$$
$$x_{19} = 81.7035764585142$$
$$x_{20} = 75.4220778711379$$
$$x_{21} = 94.2672035142578$$
$$x_{22} = 12.6687201304769$$
$$x_{23} = -1.77810988385759$$
$$x_{24} = 62.8599964822152$$
$$x_{25} = -94.2702717458136$$
$$x_{26} = 6.43748560224016$$
$$x_{27} = -31.4880803517962$$
$$x_{28} = 87.9852989815678$$
$$x_{29} = -56.5871516552196$$
$$x_{30} = -18.9751325961568$$
$$x_{31} = -62.8662782477935$$
$$x_{32} = 37.7431608214804$$
$$x_{33} = -50.3090917332535$$
$$x_{34} = 0.672717116300184$$
$$x_{35} = 31.4672625504045$$
Puntos máximos de la función:
$$x_{35} = -53.4410077699145$$
$$x_{35} = 72.2871602270437$$
$$x_{35} = -59.7208761622848$$
$$x_{35} = -66.001338580364$$
$$x_{35} = 40.8973432278724$$
$$x_{35} = -72.2822481243589$$
$$x_{35} = 78.5677422051829$$
$$x_{35} = -78.563502726215$$
$$x_{35} = 97.4115904152189$$
$$x_{35} = -40.884054909174$$
$$x_{35} = -15.8067010908366$$
$$x_{35} = -91.1267738597789$$
$$x_{35} = 15.871906339153$$
$$x_{35} = -3.4855577220419$$
$$x_{35} = 59.7277486157697$$
$$x_{35} = -9.57178791799043$$
$$x_{35} = -47.1619528823701$$
$$x_{35} = 53.4493547996909$$
$$x_{35} = -84.8450292391343$$
$$x_{35} = 9.71336796192775$$
$$x_{35} = 22.1036243063686$$
$$x_{35} = 34.6255785634057$$
$$x_{35} = -22.0658159146584$$
$$x_{35} = 47.172329623982$$
$$x_{35} = -34.6078835525902$$
$$x_{35} = 91.1300326089527$$
$$x_{35} = 28.3593255982933$$
$$x_{35} = 84.8487286205416$$
$$x_{35} = -28.3344594475311$$
$$x_{35} = -97.408696123488$$
$$x_{35} = 66.0071040861331$$
Decrece en los intervalos
$$\left[100.549257995514, \infty\right)$$
Crece en los intervalos
$$\left(-\infty, -106.833892440804\right]$$
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
$$y = \lim_{x \to -\infty}\left(\left(6 x + \left(- x^{2} \cdot 2 \frac{\cos{\left(x \right)}}{\log{\left(\left|{- x + \tan{\left(x \right)}}\right| \right)}} + \left|{x - \frac{1}{x^{2}}}\right|\right)\right) + 9\right)$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = \lim_{x \to \infty}\left(\left(6 x + \left(- x^{2} \cdot 2 \frac{\cos{\left(x \right)}}{\log{\left(\left|{- x + \tan{\left(x \right)}}\right| \right)}} + \left|{x - \frac{1}{x^{2}}}\right|\right)\right) + 9\right)$$
True
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
$$y = \lim_{x \to -\infty}\left(\left(6 x + \left(- x^{2} \cdot 2 \frac{\cos{\left(x \right)}}{\log{\left(\left|{- x + \tan{\left(x \right)}}\right| \right)}} + \left|{x - \frac{1}{x^{2}}}\right|\right)\right) + 9\right)$$
True
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = \lim_{x \to \infty}\left(\left(6 x + \left(- x^{2} \cdot 2 \frac{\cos{\left(x \right)}}{\log{\left(\left|{- x + \tan{\left(x \right)}}\right| \right)}} + \left|{x - \frac{1}{x^{2}}}\right|\right)\right) + 9\right)$$
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función |x - 1/x^2| - (cos(x)/log(Abs(tan(x) - x)))*2*x^2 + 6*x + 9, dividida por x con x->+oo y x ->-oo
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
$$y = x \lim_{x \to -\infty}\left(\frac{\left(6 x + \left(- x^{2} \cdot 2 \frac{\cos{\left(x \right)}}{\log{\left(\left|{- x + \tan{\left(x \right)}}\right| \right)}} + \left|{x - \frac{1}{x^{2}}}\right|\right)\right) + 9}{x}\right)$$
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
$$y = x \lim_{x \to \infty}\left(\frac{\left(6 x + \left(- x^{2} \cdot 2 \frac{\cos{\left(x \right)}}{\log{\left(\left|{- x + \tan{\left(x \right)}}\right| \right)}} + \left|{x - \frac{1}{x^{2}}}\right|\right)\right) + 9}{x}\right)$$
True
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
$$y = x \lim_{x \to -\infty}\left(\frac{\left(6 x + \left(- x^{2} \cdot 2 \frac{\cos{\left(x \right)}}{\log{\left(\left|{- x + \tan{\left(x \right)}}\right| \right)}} + \left|{x - \frac{1}{x^{2}}}\right|\right)\right) + 9}{x}\right)$$
True
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
$$y = x \lim_{x \to \infty}\left(\frac{\left(6 x + \left(- x^{2} \cdot 2 \frac{\cos{\left(x \right)}}{\log{\left(\left|{- x + \tan{\left(x \right)}}\right| \right)}} + \left|{x - \frac{1}{x^{2}}}\right|\right)\right) + 9}{x}\right)$$
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:
$$\left(6 x + \left(- x^{2} \cdot 2 \frac{\cos{\left(x \right)}}{\log{\left(\left|{- x + \tan{\left(x \right)}}\right| \right)}} + \left|{x - \frac{1}{x^{2}}}\right|\right)\right) + 9 = - \frac{2 x^{2} \cos{\left(x \right)}}{\log{\left(\left|{x - \tan{\left(x \right)}}\right| \right)}} - 6 x + \left|{x + \frac{1}{x^{2}}}\right| + 9$$
- No
$$\left(6 x + \left(- x^{2} \cdot 2 \frac{\cos{\left(x \right)}}{\log{\left(\left|{- x + \tan{\left(x \right)}}\right| \right)}} + \left|{x - \frac{1}{x^{2}}}\right|\right)\right) + 9 = \frac{2 x^{2} \cos{\left(x \right)}}{\log{\left(\left|{x - \tan{\left(x \right)}}\right| \right)}} + 6 x - \left|{x + \frac{1}{x^{2}}}\right| - 9$$
- No
es decir, función
no es
par ni impar
Pues, comprobamos:
$$\left(6 x + \left(- x^{2} \cdot 2 \frac{\cos{\left(x \right)}}{\log{\left(\left|{- x + \tan{\left(x \right)}}\right| \right)}} + \left|{x - \frac{1}{x^{2}}}\right|\right)\right) + 9 = - \frac{2 x^{2} \cos{\left(x \right)}}{\log{\left(\left|{x - \tan{\left(x \right)}}\right| \right)}} - 6 x + \left|{x + \frac{1}{x^{2}}}\right| + 9$$
- No
$$\left(6 x + \left(- x^{2} \cdot 2 \frac{\cos{\left(x \right)}}{\log{\left(\left|{- x + \tan{\left(x \right)}}\right| \right)}} + \left|{x - \frac{1}{x^{2}}}\right|\right)\right) + 9 = \frac{2 x^{2} \cos{\left(x \right)}}{\log{\left(\left|{x - \tan{\left(x \right)}}\right| \right)}} + 6 x - \left|{x + \frac{1}{x^{2}}}\right| - 9$$
- No
es decir, función
no es
par ni impar