Sr Examen
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 =:
-
y=(x+1)^3
-
y=2x
-
2*x^3-3*x
-
3-x^2
-
Expresiones idénticas
- abs((- cero . setenta y cinco *(sinc(uno . cinco *(x- tres . cinco)))^ dos)-(cero . setenta y cinco *(sinc(uno . cinco *(x+ tres . cinco)))^ dos)+(sinc(uno . cinco *(x- tres)))^ dos)
- abs(( menos 0.75 multiplicar por ( seno de c(1.5 multiplicar por (x menos 3.5))) al cuadrado ) menos (0.75 multiplicar por ( seno de c(1.5 multiplicar por (x más 3.5))) al cuadrado ) más ( seno de c(1.5 multiplicar por (x menos 3))) al cuadrado )
- abs(( menos cero . setenta y cinco multiplicar por ( seno de c(uno . cinco multiplicar por (x menos tres . cinco))) en el grado dos) menos (cero . setenta y cinco multiplicar por ( seno de c(uno . cinco multiplicar por (x más tres . cinco))) en el grado dos) más ( seno de c(uno . cinco multiplicar por (x menos tres))) en el grado dos)
- abs((-0.75*(sinc(1.5*(x-3.5)))2)-(0.75*(sinc(1.5*(x+3.5)))2)+(sinc(1.5*(x-3)))2)
- abs-0.75*sinc1.5*x-3.52-0.75*sinc1.5*x+3.52+sinc1.5*x-32
- abs((-0.75*(sinc(1.5*(x-3.5)))²)-(0.75*(sinc(1.5*(x+3.5)))²)+(sinc(1.5*(x-3)))²)
- abs((-0.75*(sinc(1.5*(x-3.5))) en el grado 2)-(0.75*(sinc(1.5*(x+3.5))) en el grado 2)+(sinc(1.5*(x-3))) en el grado 2)
- abs((-0.75(sinc(1.5(x-3.5)))^2)-(0.75(sinc(1.5(x+3.5)))^2)+(sinc(1.5(x-3)))^2)
- abs((-0.75(sinc(1.5(x-3.5)))2)-(0.75(sinc(1.5(x+3.5)))2)+(sinc(1.5(x-3)))2)
- abs-0.75sinc1.5x-3.52-0.75sinc1.5x+3.52+sinc1.5x-32
- abs-0.75sinc1.5x-3.5^2-0.75sinc1.5x+3.5^2+sinc1.5x-3^2
-
Expresiones semejantes
- abs((0.75*(sinc(1.5*(x-3.5)))^2)-(0.75*(sinc(1.5*(x+3.5)))^2)+(sinc(1.5*(x-3)))^2)
- abs((-0.75*(sinc(1.5*(x-3.5)))^2)-(0.75*(sinc(1.5*(x+3.5)))^2)+(sinc(1.5*(x+3)))^2)
- abs((-0.75*(sinc(1.5*(x+3.5)))^2)-(0.75*(sinc(1.5*(x+3.5)))^2)+(sinc(1.5*(x-3)))^2)
- abs((-0.75*(sinc(1.5*(x-3.5)))^2)-(0.75*(sinc(1.5*(x+3.5)))^2)-(sinc(1.5*(x-3)))^2)
- abs((-0.75*(sinc(1.5*(x-3.5)))^2)+(0.75*(sinc(1.5*(x+3.5)))^2)+(sinc(1.5*(x-3)))^2)
- abs((-0.75*(sinc(1.5*(x-3.5)))^2)-(0.75*(sinc(1.5*(x-3.5)))^2)+(sinc(1.5*(x-3)))^2)
-
Expresiones con funciones
- abs
- abs(x)*x+abs(x)-4*x
- abs(1-e^(-x))
- abs(3/x)
- abs((x^2-4)/(x^2+1))
- abs(x)*x+3*abs(x)-5x
- sinc
- sinc(e)+sin(2*x)
- sinc
- sinc(e)+sin(2*x)
- sinc
- sinc(e)+sin(2*x)
Trazado el gráfico de la función/
abs((-0.75*(sinc(1.5*(x-3.5)))^2)-(0.75*(sinc(1.5*(x+3.5)))^2)+(sinc(1.5*(x-3)))^2)
Gráfico de la función y = abs((-0.75*(sinc(1.5*(x-3.5)))^2)-(0.75*(sinc(1.5*(x+3.5)))^2)+(sinc(1.5*(x-3)))^2)
Solución
Ha introducido
[src]
| 2/3*(x - 7/2)\ 2/3*(x + 7/2)\ |
| 3*sinc |-----------| 3*sinc |-----------| |
| \ 2 / \ 2 / 2/3*(x - 3)\|
f(x) = |- -------------------- - -------------------- + sinc |---------||
| 4 4 \ 2 /|
$$f{\left(x \right)} = \left|{\left(- \frac{3 \operatorname{sinc}^{2}{\left(\frac{3 \left(x - \frac{7}{2}\right)}{2} \right)}}{4} - \frac{3 \operatorname{sinc}^{2}{\left(\frac{3 \left(x + \frac{7}{2}\right)}{2} \right)}}{4}\right) + \operatorname{sinc}^{2}{\left(\frac{3 \left(x - 3\right)}{2} \right)}}\right|$$
f = Abs(-3*sinc(3*(x - 7/2)/2)^2/4 - 3*sinc(3*(x + 7/2)/2)^2/4 + sinc(3*(x - 3)/2)^2)
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:
$$\left|{\left(- \frac{3 \operatorname{sinc}^{2}{\left(\frac{3 \left(x - \frac{7}{2}\right)}{2} \right)}}{4} - \frac{3 \operatorname{sinc}^{2}{\left(\frac{3 \left(x + \frac{7}{2}\right)}{2} \right)}}{4}\right) + \operatorname{sinc}^{2}{\left(\frac{3 \left(x - 3\right)}{2} \right)}}\right| = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución numérica
$$x_{1} = 100.394037282366$$
$$x_{2} = 332.555047742897$$
$$x_{3} = 47.4538361440148$$
$$x_{4} = 24.3259493353367$$
$$x_{5} = 56.4884250077739$$
$$x_{6} = 85.7541234898336$$
$$x_{7} = 78.9401943620084$$
$$x_{8} = 60.6676589780336$$
$$x_{9} = 106.207461097835$$
$$x_{10} = 18.0068082447106$$
$$x_{11} = 292.938569727671$$
$$x_{12} = 15.8988338269298$$
$$x_{13} = 171.534154894805$$
$$x_{14} = 53.7543355389843$$
$$x_{15} = 14.7517219207658$$
$$x_{16} = 79.481054401251$$
$$x_{17} = 1.13911874101338$$
$$x_{18} = 106.207461097836$$
$$x_{19} = 70.5471709221524$$
$$x_{20} = 66.3499114911761$$
$$x_{21} = 87.8453183531458$$
$$x_{22} = 39.7795478385081$$
$$x_{23} = 46.0436322101005$$
$$x_{24} = 75.2994819059075$$
$$x_{25} = 98.302415418474$$
$$x_{26} = 96.210857140899$$
$$x_{27} = 89.9365926024752$$
$$x_{28} = 57.9535762163171$$
$$x_{29} = 227.78200590075$$
$$x_{30} = 64.2510685391164$$
$$x_{31} = 26.4309002752638$$
$$x_{32} = 7.46368519549793$$
$$x_{33} = 68.4486095268862$$
$$x_{34} = 43.9553405987308$$
$$x_{35} = 8.47885108724205$$
$$x_{36} = 77.3902176134121$$
$$x_{37} = 93.6241574236973$$
$$x_{38} = 73.2088525639618$$
$$x_{39} = 22.2203222288395$$
$$x_{40} = 140.144139388095$$
$$x_{41} = 376.6737367235$$
$$x_{42} = 50.220924588563$$
$$x_{43} = 6.3495216155719$$
$$x_{44} = 92.0279426795739$$
$$x_{45} = 253.165136709889$$
$$x_{46} = 16.8363384062115$$
$$x_{47} = 83.6630118030698$$
$$x_{48} = 202.633997223861$$
$$x_{49} = 41.8673066821498$$
o sea hay que resolver la ecuación:
$$\left|{\left(- \frac{3 \operatorname{sinc}^{2}{\left(\frac{3 \left(x - \frac{7}{2}\right)}{2} \right)}}{4} - \frac{3 \operatorname{sinc}^{2}{\left(\frac{3 \left(x + \frac{7}{2}\right)}{2} \right)}}{4}\right) + \operatorname{sinc}^{2}{\left(\frac{3 \left(x - 3\right)}{2} \right)}}\right| = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución numérica
$$x_{1} = 100.394037282366$$
$$x_{2} = 332.555047742897$$
$$x_{3} = 47.4538361440148$$
$$x_{4} = 24.3259493353367$$
$$x_{5} = 56.4884250077739$$
$$x_{6} = 85.7541234898336$$
$$x_{7} = 78.9401943620084$$
$$x_{8} = 60.6676589780336$$
$$x_{9} = 106.207461097835$$
$$x_{10} = 18.0068082447106$$
$$x_{11} = 292.938569727671$$
$$x_{12} = 15.8988338269298$$
$$x_{13} = 171.534154894805$$
$$x_{14} = 53.7543355389843$$
$$x_{15} = 14.7517219207658$$
$$x_{16} = 79.481054401251$$
$$x_{17} = 1.13911874101338$$
$$x_{18} = 106.207461097836$$
$$x_{19} = 70.5471709221524$$
$$x_{20} = 66.3499114911761$$
$$x_{21} = 87.8453183531458$$
$$x_{22} = 39.7795478385081$$
$$x_{23} = 46.0436322101005$$
$$x_{24} = 75.2994819059075$$
$$x_{25} = 98.302415418474$$
$$x_{26} = 96.210857140899$$
$$x_{27} = 89.9365926024752$$
$$x_{28} = 57.9535762163171$$
$$x_{29} = 227.78200590075$$
$$x_{30} = 64.2510685391164$$
$$x_{31} = 26.4309002752638$$
$$x_{32} = 7.46368519549793$$
$$x_{33} = 68.4486095268862$$
$$x_{34} = 43.9553405987308$$
$$x_{35} = 8.47885108724205$$
$$x_{36} = 77.3902176134121$$
$$x_{37} = 93.6241574236973$$
$$x_{38} = 73.2088525639618$$
$$x_{39} = 22.2203222288395$$
$$x_{40} = 140.144139388095$$
$$x_{41} = 376.6737367235$$
$$x_{42} = 50.220924588563$$
$$x_{43} = 6.3495216155719$$
$$x_{44} = 92.0279426795739$$
$$x_{45} = 253.165136709889$$
$$x_{46} = 16.8363384062115$$
$$x_{47} = 83.6630118030698$$
$$x_{48} = 202.633997223861$$
$$x_{49} = 41.8673066821498$$
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
$$\frac{\left(\left(- \frac{3 \operatorname{re}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{21}{4} \right)}\right)} \operatorname{im}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{21}{4} \right)}\right)}}{2} + 2 \operatorname{re}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{9}{2} \right)}\right)} \operatorname{im}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{9}{2} \right)}\right)} - \frac{3 \operatorname{re}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} + \frac{21}{4} \right)}\right)} \operatorname{im}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} + \frac{21}{4} \right)}\right)}}{2}\right) \left(- \frac{9 \operatorname{re}{\left(\begin{cases} \frac{4 \left(\frac{3 \left(x - \frac{7}{2}\right) \cos{\left(\frac{3 x}{2} - \frac{21}{4} \right)}}{2} - \sin{\left(\frac{3 x}{2} - \frac{21}{4} \right)}\right)}{9 \left(x - \frac{7}{2}\right)^{2}} & \text{for}\: \frac{3 x}{2} - \frac{21}{4} \neq 0 \\0 & \text{otherwise} \end{cases}\right)} \operatorname{im}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{21}{4} \right)}\right)}}{4} + 3 \operatorname{re}{\left(\begin{cases} \frac{4 \left(\frac{3 \left(x - 3\right) \cos{\left(\frac{3 x}{2} - \frac{9}{2} \right)}}{2} - \sin{\left(\frac{3 x}{2} - \frac{9}{2} \right)}\right)}{9 \left(x - 3\right)^{2}} & \text{for}\: \frac{3 x}{2} - \frac{9}{2} \neq 0 \\0 & \text{otherwise} \end{cases}\right)} \operatorname{im}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{9}{2} \right)}\right)} - \frac{9 \operatorname{re}{\left(\begin{cases} \frac{4 \left(\frac{3 \left(x + \frac{7}{2}\right) \cos{\left(\frac{3 x}{2} + \frac{21}{4} \right)}}{2} - \sin{\left(\frac{3 x}{2} + \frac{21}{4} \right)}\right)}{9 \left(x + \frac{7}{2}\right)^{2}} & \text{for}\: \frac{3 x}{2} + \frac{21}{4} \neq 0 \\0 & \text{otherwise} \end{cases}\right)} \operatorname{im}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} + \frac{21}{4} \right)}\right)}}{4} - \frac{9 \operatorname{re}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{21}{4} \right)}\right)} \operatorname{im}{\left(\begin{cases} \frac{4 \left(\frac{3 \left(x - \frac{7}{2}\right) \cos{\left(\frac{3 x}{2} - \frac{21}{4} \right)}}{2} - \sin{\left(\frac{3 x}{2} - \frac{21}{4} \right)}\right)}{9 \left(x - \frac{7}{2}\right)^{2}} & \text{for}\: \frac{3 x}{2} - \frac{21}{4} \neq 0 \\0 & \text{otherwise} \end{cases}\right)}}{4} + 3 \operatorname{re}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{9}{2} \right)}\right)} \operatorname{im}{\left(\begin{cases} \frac{4 \left(\frac{3 \left(x - 3\right) \cos{\left(\frac{3 x}{2} - \frac{9}{2} \right)}}{2} - \sin{\left(\frac{3 x}{2} - \frac{9}{2} \right)}\right)}{9 \left(x - 3\right)^{2}} & \text{for}\: \frac{3 x}{2} - \frac{9}{2} \neq 0 \\0 & \text{otherwise} \end{cases}\right)} - \frac{9 \operatorname{re}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} + \frac{21}{4} \right)}\right)} \operatorname{im}{\left(\begin{cases} \frac{4 \left(\frac{3 \left(x + \frac{7}{2}\right) \cos{\left(\frac{3 x}{2} + \frac{21}{4} \right)}}{2} - \sin{\left(\frac{3 x}{2} + \frac{21}{4} \right)}\right)}{9 \left(x + \frac{7}{2}\right)^{2}} & \text{for}\: \frac{3 x}{2} + \frac{21}{4} \neq 0 \\0 & \text{otherwise} \end{cases}\right)}}{4}\right) + \left(- \frac{9 \operatorname{re}{\left(\begin{cases} \frac{4 \left(\frac{3 \left(x - \frac{7}{2}\right) \cos{\left(\frac{3 x}{2} - \frac{21}{4} \right)}}{2} - \sin{\left(\frac{3 x}{2} - \frac{21}{4} \right)}\right)}{9 \left(x - \frac{7}{2}\right)^{2}} & \text{for}\: \frac{3 x}{2} - \frac{21}{4} \neq 0 \\0 & \text{otherwise} \end{cases}\right)} \operatorname{re}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{21}{4} \right)}\right)}}{4} + 3 \operatorname{re}{\left(\begin{cases} \frac{4 \left(\frac{3 \left(x - 3\right) \cos{\left(\frac{3 x}{2} - \frac{9}{2} \right)}}{2} - \sin{\left(\frac{3 x}{2} - \frac{9}{2} \right)}\right)}{9 \left(x - 3\right)^{2}} & \text{for}\: \frac{3 x}{2} - \frac{9}{2} \neq 0 \\0 & \text{otherwise} \end{cases}\right)} \operatorname{re}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{9}{2} \right)}\right)} - \frac{9 \operatorname{re}{\left(\begin{cases} \frac{4 \left(\frac{3 \left(x + \frac{7}{2}\right) \cos{\left(\frac{3 x}{2} + \frac{21}{4} \right)}}{2} - \sin{\left(\frac{3 x}{2} + \frac{21}{4} \right)}\right)}{9 \left(x + \frac{7}{2}\right)^{2}} & \text{for}\: \frac{3 x}{2} + \frac{21}{4} \neq 0 \\0 & \text{otherwise} \end{cases}\right)} \operatorname{re}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} + \frac{21}{4} \right)}\right)}}{4} + \frac{9 \operatorname{im}{\left(\begin{cases} \frac{4 \left(\frac{3 \left(x - \frac{7}{2}\right) \cos{\left(\frac{3 x}{2} - \frac{21}{4} \right)}}{2} - \sin{\left(\frac{3 x}{2} - \frac{21}{4} \right)}\right)}{9 \left(x - \frac{7}{2}\right)^{2}} & \text{for}\: \frac{3 x}{2} - \frac{21}{4} \neq 0 \\0 & \text{otherwise} \end{cases}\right)} \operatorname{im}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{21}{4} \right)}\right)}}{4} - 3 \operatorname{im}{\left(\begin{cases} \frac{4 \left(\frac{3 \left(x - 3\right) \cos{\left(\frac{3 x}{2} - \frac{9}{2} \right)}}{2} - \sin{\left(\frac{3 x}{2} - \frac{9}{2} \right)}\right)}{9 \left(x - 3\right)^{2}} & \text{for}\: \frac{3 x}{2} - \frac{9}{2} \neq 0 \\0 & \text{otherwise} \end{cases}\right)} \operatorname{im}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{9}{2} \right)}\right)} + \frac{9 \operatorname{im}{\left(\begin{cases} \frac{4 \left(\frac{3 \left(x + \frac{7}{2}\right) \cos{\left(\frac{3 x}{2} + \frac{21}{4} \right)}}{2} - \sin{\left(\frac{3 x}{2} + \frac{21}{4} \right)}\right)}{9 \left(x + \frac{7}{2}\right)^{2}} & \text{for}\: \frac{3 x}{2} + \frac{21}{4} \neq 0 \\0 & \text{otherwise} \end{cases}\right)} \operatorname{im}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} + \frac{21}{4} \right)}\right)}}{4}\right) \left(- \frac{3 \left(\operatorname{re}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{21}{4} \right)}\right)}\right)^{2}}{4} + \left(\operatorname{re}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{9}{2} \right)}\right)}\right)^{2} - \frac{3 \left(\operatorname{re}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} + \frac{21}{4} \right)}\right)}\right)^{2}}{4} + \frac{3 \left(\operatorname{im}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{21}{4} \right)}\right)}\right)^{2}}{4} - \left(\operatorname{im}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{9}{2} \right)}\right)}\right)^{2} + \frac{3 \left(\operatorname{im}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} + \frac{21}{4} \right)}\right)}\right)^{2}}{4}\right)\right) \operatorname{sign}{\left(\frac{3 \operatorname{sinc}^{2}{\left(\frac{3 x}{2} - \frac{21}{4} \right)}}{4} - \operatorname{sinc}^{2}{\left(\frac{3 x}{2} - \frac{9}{2} \right)} + \frac{3 \operatorname{sinc}^{2}{\left(\frac{3 x}{2} + \frac{21}{4} \right)}}{4} \right)}}{\frac{3 \operatorname{sinc}^{2}{\left(\frac{3 x}{2} - \frac{21}{4} \right)}}{4} - \operatorname{sinc}^{2}{\left(\frac{3 x}{2} - \frac{9}{2} \right)} + \frac{3 \operatorname{sinc}^{2}{\left(\frac{3 x}{2} + \frac{21}{4} \right)}}{4}} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = -25.2891830586486$$
$$x_{2} = 10.0413977591473$$
$$x_{3} = -24.5240066237629$$
$$x_{4} = -33.9676954985314$$
$$x_{5} = -13.9920612178121$$
$$x_{6} = -51.6701521437033$$
$$x_{7} = -57.9563573415376$$
$$x_{8} = 81.30418750723$$
$$x_{9} = -93.5678237386056$$
$$x_{10} = 56.1694022547987$$
$$x_{11} = 38.3591097543705$$
$$x_{12} = -38.114982279046$$
$$x_{13} = -18.1915200799956$$
$$x_{14} = 51.980025552783$$
$$x_{15} = -30.0321420491974$$
$$x_{16} = -90.435387981693$$
$$x_{17} = -86.246911706429$$
$$x_{18} = -82.0585032601189$$
$$x_{19} = 82.3479453186041$$
$$x_{20} = 84.4424852259481$$
$$x_{21} = 40.4541360154989$$
$$x_{22} = -95.6624117412458$$
$$x_{23} = -40.1999226246919$$
$$x_{24} = -73.6819803901426$$
$$x_{25} = 70.8315760569921$$
$$x_{26} = -7.69628941684326$$
$$x_{27} = -75.7760648726363$$
$$x_{28} = 36.2640086520819$$
$$x_{29} = -69.4939368365511$$
$$x_{30} = -60.0515160044936$$
$$x_{31} = -77.8701831725522$$
$$x_{32} = 12.1491641598531$$
$$x_{33} = 86.5370184030478$$
$$x_{34} = 27.8824805114201$$
$$x_{35} = -36.035537667834$$
$$x_{36} = 60.3586810642082$$
$$x_{37} = 7.9231607457098$$
$$x_{38} = -55.8610947638737$$
$$x_{39} = -91.4732243467267$$
$$x_{40} = 2.55352749832256$$
$$x_{41} = 44.6440085282705$$
$$x_{42} = -42.2878728663535$$
$$x_{43} = 64.5478832428738$$
$$x_{44} = -43.2850467361486$$
$$x_{45} = 69.7805312521359$$
$$x_{46} = 32.0735179028996$$
$$x_{47} = 93.8710955963389$$
$$x_{48} = 95.9655634340815$$
$$x_{49} = -79.9643306018706$$
$$x_{50} = 100.154487776243$$
$$x_{51} = -31.9311177846054$$
$$x_{52} = -11.8934260810529$$
$$x_{53} = -9.79492708855456$$
$$x_{54} = 29.97808355276$$
$$x_{55} = 80.2533981643314$$
$$x_{56} = 14.252130607825$$
$$x_{57} = 73.969707174174$$
$$x_{58} = -53.7657039727558$$
$$x_{59} = 20.5489679565243$$
$$x_{60} = -47.4783636242956$$
$$x_{61} = 58.2640524116865$$
$$x_{62} = 98.0600274007149$$
$$x_{63} = -62.1465891503376$$
$$x_{64} = -1.43269912489468$$
$$x_{65} = 99.104099575324$$
$$x_{66} = 18.4512432534799$$
$$x_{67} = 0.00472098936395306$$
$$x_{68} = 4.30900298154749$$
$$x_{69} = -64.2415909824392$$
$$x_{70} = -99.8515572836021$$
$$x_{71} = 16.3524809521568$$
$$x_{72} = 54.0747277498394$$
$$x_{73} = 76.0642797634986$$
$$x_{74} = -97.7569893072304$$
$$x_{75} = -65.3061151927489$$
$$x_{76} = 78.1588431910444$$
$$x_{77} = -49.5743937481977$$
$$x_{78} = 71.8751246325107$$
$$x_{79} = 62.4532906443319$$
$$x_{80} = -5.59746589889974$$
$$x_{81} = -46.4685753542707$$
$$x_{82} = 6.83844024747099$$
$$x_{83} = -20.2941180583011$$
$$x_{84} = -84.1526978798189$$
$$x_{85} = -16.0912222804048$$
$$x_{86} = 34.1688177968469$$
$$x_{87} = 49.88529170716$$
$$x_{88} = -23.2694212516523$$
$$x_{89} = 42.5490991571084$$
$$x_{90} = -3.49813986553354$$
$$x_{91} = -71.5879354016358$$
$$x_{92} = 88.6315453178178$$
$$x_{93} = 25.7866614841729$$
$$x_{94} = 91.7766235790219$$
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:
$$x_{1} = -24.5240066237629$$
$$x_{2} = -33.9676954985314$$
$$x_{3} = -13.9920612178121$$
$$x_{4} = -38.114982279046$$
$$x_{5} = -18.1915200799956$$
$$x_{6} = -30.0321420491974$$
$$x_{7} = -90.435387981693$$
$$x_{8} = -86.246911706429$$
$$x_{9} = -82.0585032601189$$
$$x_{10} = -40.1999226246919$$
$$x_{11} = -73.6819803901426$$
$$x_{12} = -7.69628941684326$$
$$x_{13} = -75.7760648726363$$
$$x_{14} = -69.4939368365511$$
$$x_{15} = -77.8701831725522$$
$$x_{16} = -36.035537667834$$
$$x_{17} = -42.2878728663535$$
$$x_{18} = -79.9643306018706$$
$$x_{19} = -31.9311177846054$$
$$x_{20} = -11.8934260810529$$
$$x_{21} = -9.79492708855456$$
$$x_{22} = -1.43269912489468$$
$$x_{23} = -65.3061151927489$$
$$x_{24} = -5.59746589889974$$
$$x_{25} = -46.4685753542707$$
$$x_{26} = -20.2941180583011$$
$$x_{27} = -84.1526978798189$$
$$x_{28} = -16.0912222804048$$
$$x_{29} = -71.5879354016358$$
Puntos máximos de la función:
$$x_{29} = -25.2891830586486$$
$$x_{29} = 10.0413977591473$$
$$x_{29} = -51.6701521437033$$
$$x_{29} = -57.9563573415376$$
$$x_{29} = 81.30418750723$$
$$x_{29} = -93.5678237386056$$
$$x_{29} = 56.1694022547987$$
$$x_{29} = 38.3591097543705$$
$$x_{29} = 51.980025552783$$
$$x_{29} = 82.3479453186041$$
$$x_{29} = 84.4424852259481$$
$$x_{29} = 40.4541360154989$$
$$x_{29} = -95.6624117412458$$
$$x_{29} = 70.8315760569921$$
$$x_{29} = 36.2640086520819$$
$$x_{29} = -60.0515160044936$$
$$x_{29} = 12.1491641598531$$
$$x_{29} = 86.5370184030478$$
$$x_{29} = 27.8824805114201$$
$$x_{29} = 60.3586810642082$$
$$x_{29} = 7.9231607457098$$
$$x_{29} = -55.8610947638737$$
$$x_{29} = -91.4732243467267$$
$$x_{29} = 2.55352749832256$$
$$x_{29} = 44.6440085282705$$
$$x_{29} = 64.5478832428738$$
$$x_{29} = -43.2850467361486$$
$$x_{29} = 69.7805312521359$$
$$x_{29} = 32.0735179028996$$
$$x_{29} = 93.8710955963389$$
$$x_{29} = 95.9655634340815$$
$$x_{29} = 100.154487776243$$
$$x_{29} = 29.97808355276$$
$$x_{29} = 80.2533981643314$$
$$x_{29} = 14.252130607825$$
$$x_{29} = 73.969707174174$$
$$x_{29} = -53.7657039727558$$
$$x_{29} = 20.5489679565243$$
$$x_{29} = -47.4783636242956$$
$$x_{29} = 58.2640524116865$$
$$x_{29} = 98.0600274007149$$
$$x_{29} = -62.1465891503376$$
$$x_{29} = 99.104099575324$$
$$x_{29} = 18.4512432534799$$
$$x_{29} = 0.00472098936395306$$
$$x_{29} = 4.30900298154749$$
$$x_{29} = -64.2415909824392$$
$$x_{29} = -99.8515572836021$$
$$x_{29} = 16.3524809521568$$
$$x_{29} = 54.0747277498394$$
$$x_{29} = 76.0642797634986$$
$$x_{29} = -97.7569893072304$$
$$x_{29} = 78.1588431910444$$
$$x_{29} = -49.5743937481977$$
$$x_{29} = 71.8751246325107$$
$$x_{29} = 62.4532906443319$$
$$x_{29} = 6.83844024747099$$
$$x_{29} = 34.1688177968469$$
$$x_{29} = 49.88529170716$$
$$x_{29} = -23.2694212516523$$
$$x_{29} = 42.5490991571084$$
$$x_{29} = -3.49813986553354$$
$$x_{29} = 88.6315453178178$$
$$x_{29} = 25.7866614841729$$
$$x_{29} = 91.7766235790219$$
Decrece en los intervalos
$$\left[-1.43269912489468, \infty\right)$$
Crece en los intervalos
$$\left(-\infty, -90.435387981693\right]$$
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(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
$$\frac{\left(\left(- \frac{3 \operatorname{re}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{21}{4} \right)}\right)} \operatorname{im}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{21}{4} \right)}\right)}}{2} + 2 \operatorname{re}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{9}{2} \right)}\right)} \operatorname{im}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{9}{2} \right)}\right)} - \frac{3 \operatorname{re}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} + \frac{21}{4} \right)}\right)} \operatorname{im}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} + \frac{21}{4} \right)}\right)}}{2}\right) \left(- \frac{9 \operatorname{re}{\left(\begin{cases} \frac{4 \left(\frac{3 \left(x - \frac{7}{2}\right) \cos{\left(\frac{3 x}{2} - \frac{21}{4} \right)}}{2} - \sin{\left(\frac{3 x}{2} - \frac{21}{4} \right)}\right)}{9 \left(x - \frac{7}{2}\right)^{2}} & \text{for}\: \frac{3 x}{2} - \frac{21}{4} \neq 0 \\0 & \text{otherwise} \end{cases}\right)} \operatorname{im}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{21}{4} \right)}\right)}}{4} + 3 \operatorname{re}{\left(\begin{cases} \frac{4 \left(\frac{3 \left(x - 3\right) \cos{\left(\frac{3 x}{2} - \frac{9}{2} \right)}}{2} - \sin{\left(\frac{3 x}{2} - \frac{9}{2} \right)}\right)}{9 \left(x - 3\right)^{2}} & \text{for}\: \frac{3 x}{2} - \frac{9}{2} \neq 0 \\0 & \text{otherwise} \end{cases}\right)} \operatorname{im}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{9}{2} \right)}\right)} - \frac{9 \operatorname{re}{\left(\begin{cases} \frac{4 \left(\frac{3 \left(x + \frac{7}{2}\right) \cos{\left(\frac{3 x}{2} + \frac{21}{4} \right)}}{2} - \sin{\left(\frac{3 x}{2} + \frac{21}{4} \right)}\right)}{9 \left(x + \frac{7}{2}\right)^{2}} & \text{for}\: \frac{3 x}{2} + \frac{21}{4} \neq 0 \\0 & \text{otherwise} \end{cases}\right)} \operatorname{im}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} + \frac{21}{4} \right)}\right)}}{4} - \frac{9 \operatorname{re}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{21}{4} \right)}\right)} \operatorname{im}{\left(\begin{cases} \frac{4 \left(\frac{3 \left(x - \frac{7}{2}\right) \cos{\left(\frac{3 x}{2} - \frac{21}{4} \right)}}{2} - \sin{\left(\frac{3 x}{2} - \frac{21}{4} \right)}\right)}{9 \left(x - \frac{7}{2}\right)^{2}} & \text{for}\: \frac{3 x}{2} - \frac{21}{4} \neq 0 \\0 & \text{otherwise} \end{cases}\right)}}{4} + 3 \operatorname{re}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{9}{2} \right)}\right)} \operatorname{im}{\left(\begin{cases} \frac{4 \left(\frac{3 \left(x - 3\right) \cos{\left(\frac{3 x}{2} - \frac{9}{2} \right)}}{2} - \sin{\left(\frac{3 x}{2} - \frac{9}{2} \right)}\right)}{9 \left(x - 3\right)^{2}} & \text{for}\: \frac{3 x}{2} - \frac{9}{2} \neq 0 \\0 & \text{otherwise} \end{cases}\right)} - \frac{9 \operatorname{re}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} + \frac{21}{4} \right)}\right)} \operatorname{im}{\left(\begin{cases} \frac{4 \left(\frac{3 \left(x + \frac{7}{2}\right) \cos{\left(\frac{3 x}{2} + \frac{21}{4} \right)}}{2} - \sin{\left(\frac{3 x}{2} + \frac{21}{4} \right)}\right)}{9 \left(x + \frac{7}{2}\right)^{2}} & \text{for}\: \frac{3 x}{2} + \frac{21}{4} \neq 0 \\0 & \text{otherwise} \end{cases}\right)}}{4}\right) + \left(- \frac{9 \operatorname{re}{\left(\begin{cases} \frac{4 \left(\frac{3 \left(x - \frac{7}{2}\right) \cos{\left(\frac{3 x}{2} - \frac{21}{4} \right)}}{2} - \sin{\left(\frac{3 x}{2} - \frac{21}{4} \right)}\right)}{9 \left(x - \frac{7}{2}\right)^{2}} & \text{for}\: \frac{3 x}{2} - \frac{21}{4} \neq 0 \\0 & \text{otherwise} \end{cases}\right)} \operatorname{re}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{21}{4} \right)}\right)}}{4} + 3 \operatorname{re}{\left(\begin{cases} \frac{4 \left(\frac{3 \left(x - 3\right) \cos{\left(\frac{3 x}{2} - \frac{9}{2} \right)}}{2} - \sin{\left(\frac{3 x}{2} - \frac{9}{2} \right)}\right)}{9 \left(x - 3\right)^{2}} & \text{for}\: \frac{3 x}{2} - \frac{9}{2} \neq 0 \\0 & \text{otherwise} \end{cases}\right)} \operatorname{re}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{9}{2} \right)}\right)} - \frac{9 \operatorname{re}{\left(\begin{cases} \frac{4 \left(\frac{3 \left(x + \frac{7}{2}\right) \cos{\left(\frac{3 x}{2} + \frac{21}{4} \right)}}{2} - \sin{\left(\frac{3 x}{2} + \frac{21}{4} \right)}\right)}{9 \left(x + \frac{7}{2}\right)^{2}} & \text{for}\: \frac{3 x}{2} + \frac{21}{4} \neq 0 \\0 & \text{otherwise} \end{cases}\right)} \operatorname{re}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} + \frac{21}{4} \right)}\right)}}{4} + \frac{9 \operatorname{im}{\left(\begin{cases} \frac{4 \left(\frac{3 \left(x - \frac{7}{2}\right) \cos{\left(\frac{3 x}{2} - \frac{21}{4} \right)}}{2} - \sin{\left(\frac{3 x}{2} - \frac{21}{4} \right)}\right)}{9 \left(x - \frac{7}{2}\right)^{2}} & \text{for}\: \frac{3 x}{2} - \frac{21}{4} \neq 0 \\0 & \text{otherwise} \end{cases}\right)} \operatorname{im}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{21}{4} \right)}\right)}}{4} - 3 \operatorname{im}{\left(\begin{cases} \frac{4 \left(\frac{3 \left(x - 3\right) \cos{\left(\frac{3 x}{2} - \frac{9}{2} \right)}}{2} - \sin{\left(\frac{3 x}{2} - \frac{9}{2} \right)}\right)}{9 \left(x - 3\right)^{2}} & \text{for}\: \frac{3 x}{2} - \frac{9}{2} \neq 0 \\0 & \text{otherwise} \end{cases}\right)} \operatorname{im}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{9}{2} \right)}\right)} + \frac{9 \operatorname{im}{\left(\begin{cases} \frac{4 \left(\frac{3 \left(x + \frac{7}{2}\right) \cos{\left(\frac{3 x}{2} + \frac{21}{4} \right)}}{2} - \sin{\left(\frac{3 x}{2} + \frac{21}{4} \right)}\right)}{9 \left(x + \frac{7}{2}\right)^{2}} & \text{for}\: \frac{3 x}{2} + \frac{21}{4} \neq 0 \\0 & \text{otherwise} \end{cases}\right)} \operatorname{im}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} + \frac{21}{4} \right)}\right)}}{4}\right) \left(- \frac{3 \left(\operatorname{re}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{21}{4} \right)}\right)}\right)^{2}}{4} + \left(\operatorname{re}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{9}{2} \right)}\right)}\right)^{2} - \frac{3 \left(\operatorname{re}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} + \frac{21}{4} \right)}\right)}\right)^{2}}{4} + \frac{3 \left(\operatorname{im}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{21}{4} \right)}\right)}\right)^{2}}{4} - \left(\operatorname{im}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} - \frac{9}{2} \right)}\right)}\right)^{2} + \frac{3 \left(\operatorname{im}{\left(\operatorname{sinc}{\left(\frac{3 x}{2} + \frac{21}{4} \right)}\right)}\right)^{2}}{4}\right)\right) \operatorname{sign}{\left(\frac{3 \operatorname{sinc}^{2}{\left(\frac{3 x}{2} - \frac{21}{4} \right)}}{4} - \operatorname{sinc}^{2}{\left(\frac{3 x}{2} - \frac{9}{2} \right)} + \frac{3 \operatorname{sinc}^{2}{\left(\frac{3 x}{2} + \frac{21}{4} \right)}}{4} \right)}}{\frac{3 \operatorname{sinc}^{2}{\left(\frac{3 x}{2} - \frac{21}{4} \right)}}{4} - \operatorname{sinc}^{2}{\left(\frac{3 x}{2} - \frac{9}{2} \right)} + \frac{3 \operatorname{sinc}^{2}{\left(\frac{3 x}{2} + \frac{21}{4} \right)}}{4}} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = -25.2891830586486$$
$$x_{2} = 10.0413977591473$$
$$x_{3} = -24.5240066237629$$
$$x_{4} = -33.9676954985314$$
$$x_{5} = -13.9920612178121$$
$$x_{6} = -51.6701521437033$$
$$x_{7} = -57.9563573415376$$
$$x_{8} = 81.30418750723$$
$$x_{9} = -93.5678237386056$$
$$x_{10} = 56.1694022547987$$
$$x_{11} = 38.3591097543705$$
$$x_{12} = -38.114982279046$$
$$x_{13} = -18.1915200799956$$
$$x_{14} = 51.980025552783$$
$$x_{15} = -30.0321420491974$$
$$x_{16} = -90.435387981693$$
$$x_{17} = -86.246911706429$$
$$x_{18} = -82.0585032601189$$
$$x_{19} = 82.3479453186041$$
$$x_{20} = 84.4424852259481$$
$$x_{21} = 40.4541360154989$$
$$x_{22} = -95.6624117412458$$
$$x_{23} = -40.1999226246919$$
$$x_{24} = -73.6819803901426$$
$$x_{25} = 70.8315760569921$$
$$x_{26} = -7.69628941684326$$
$$x_{27} = -75.7760648726363$$
$$x_{28} = 36.2640086520819$$
$$x_{29} = -69.4939368365511$$
$$x_{30} = -60.0515160044936$$
$$x_{31} = -77.8701831725522$$
$$x_{32} = 12.1491641598531$$
$$x_{33} = 86.5370184030478$$
$$x_{34} = 27.8824805114201$$
$$x_{35} = -36.035537667834$$
$$x_{36} = 60.3586810642082$$
$$x_{37} = 7.9231607457098$$
$$x_{38} = -55.8610947638737$$
$$x_{39} = -91.4732243467267$$
$$x_{40} = 2.55352749832256$$
$$x_{41} = 44.6440085282705$$
$$x_{42} = -42.2878728663535$$
$$x_{43} = 64.5478832428738$$
$$x_{44} = -43.2850467361486$$
$$x_{45} = 69.7805312521359$$
$$x_{46} = 32.0735179028996$$
$$x_{47} = 93.8710955963389$$
$$x_{48} = 95.9655634340815$$
$$x_{49} = -79.9643306018706$$
$$x_{50} = 100.154487776243$$
$$x_{51} = -31.9311177846054$$
$$x_{52} = -11.8934260810529$$
$$x_{53} = -9.79492708855456$$
$$x_{54} = 29.97808355276$$
$$x_{55} = 80.2533981643314$$
$$x_{56} = 14.252130607825$$
$$x_{57} = 73.969707174174$$
$$x_{58} = -53.7657039727558$$
$$x_{59} = 20.5489679565243$$
$$x_{60} = -47.4783636242956$$
$$x_{61} = 58.2640524116865$$
$$x_{62} = 98.0600274007149$$
$$x_{63} = -62.1465891503376$$
$$x_{64} = -1.43269912489468$$
$$x_{65} = 99.104099575324$$
$$x_{66} = 18.4512432534799$$
$$x_{67} = 0.00472098936395306$$
$$x_{68} = 4.30900298154749$$
$$x_{69} = -64.2415909824392$$
$$x_{70} = -99.8515572836021$$
$$x_{71} = 16.3524809521568$$
$$x_{72} = 54.0747277498394$$
$$x_{73} = 76.0642797634986$$
$$x_{74} = -97.7569893072304$$
$$x_{75} = -65.3061151927489$$
$$x_{76} = 78.1588431910444$$
$$x_{77} = -49.5743937481977$$
$$x_{78} = 71.8751246325107$$
$$x_{79} = 62.4532906443319$$
$$x_{80} = -5.59746589889974$$
$$x_{81} = -46.4685753542707$$
$$x_{82} = 6.83844024747099$$
$$x_{83} = -20.2941180583011$$
$$x_{84} = -84.1526978798189$$
$$x_{85} = -16.0912222804048$$
$$x_{86} = 34.1688177968469$$
$$x_{87} = 49.88529170716$$
$$x_{88} = -23.2694212516523$$
$$x_{89} = 42.5490991571084$$
$$x_{90} = -3.49813986553354$$
$$x_{91} = -71.5879354016358$$
$$x_{92} = 88.6315453178178$$
$$x_{93} = 25.7866614841729$$
$$x_{94} = 91.7766235790219$$
Signos de extremos en los puntos:
(-25.289183058648614, 0.000290887511214878)
(10.041397759147275, 0.00447454788199126)
(-24.524006623762943, 0.000269335259671835)
(-33.96769549853142, 0.000121165972855274)
(-13.992061217812068, 0.000686387800900466)
(-51.67015214370332, 6.95655050337903e-5)
(-57.95635734153756, 5.60908147020173e-5)
(81.30418750723004, 6.31164573396052e-6)
(-93.56782373860558, 2.25186905168671e-5)
(56.169402254798655, 2.04420274363666e-5)
(38.35910975437053, 0.000176150994449236)
(-38.11498227904597, 8.57604826363119e-5)
(-18.191520079995552, 0.000447673939826009)
(51.980025552783, 2.60669403475587e-5)
(-30.032142049197397, 0.000177520018855539)
(-90.43538798169297, 6.92721317050443e-6)
(-86.246911706429, 7.92934269590219e-6)
(-82.05850326011887, 9.14122519148417e-6)
(82.34794531860415, 3.43106889291323e-5)
(84.44248522594815, 3.25555852540654e-5)
(40.454136015498854, 0.00015669000934503)
(-95.66241174124579, 2.15785857582007e-5)
(-40.199922624691894, 7.31830319511141e-5)
(-73.68198039014264, 1.24502254933544e-5)
(70.83157605699215, 9.81634376889774e-6)
(-7.696289416843264, 0.0016615554859328)
(-75.77606487263628, 1.14863359706328e-5)
(36.26400865208191, 0.000199476784981299)
(-69.49393683655114, 1.47373912276976e-5)
(-60.05151600449359, 5.24609661947007e-5)
(-77.87018317255219, 1.06215899081906e-5)
(12.149164159853141, 0.00240254803251788)
(86.53701840304781, 3.09317881080501e-5)
(27.88248051142007, 0.000360978002924735)
(-36.03553766783396, 0.000101427545330536)
(60.35868106420825, 1.62999431424904e-5)
(7.923160745709802, 0.0100649748022253)
(-55.8610947638737, 6.01109485502864e-5)
(-91.47322434672674, 2.35215991381138e-5)
(2.553527498322559, 0.494446087131142)
(44.64400852827055, 0.000126327568429062)
(-42.2878728663535, 6.29727045182555e-5)
(64.54788324287375, 1.31853378920751e-5)
(-43.28504673614864, 9.66410340079052e-5)
(69.78053125213593, 4.85812875775074e-5)
(32.073517902899646, 0.000262523050002875)
(93.87109559633888, 3.96067203567553e-6)
(95.96556343408155, 3.68501542005522e-6)
(-79.96433060187064, 9.84344510288572e-6)
(100.15448777624307, 3.20305128200246e-6)
(-31.931117784605426, 0.000146246037777505)
(-11.893426081052901, 0.000884524043858936)
(-9.794927088554559, 0.00118268240193787)
(29.97808355275997, 0.000305894858012071)
(80.25339816433137, 3.62116480339891e-5)
(14.252130607824956, 0.00144493396595072)
(73.96970717417399, 4.29684971106515e-5)
(-53.765703972755794, 6.45794206939285e-5)
(20.548967956524265, 0.000461221609904086)
(-47.47836362429556, 8.14407942229561e-5)
(58.2640524116865, 1.82187302788773e-5)
(98.06002740071486, 3.43331077254763e-6)
(-62.146589150337554, 4.9172456093466e-5)
(-1.4326991248946848, 0.00828832167348865)
(99.10409957532401, 2.33261124466523e-5)
(18.451243253479923, 0.000644023730084124)
(0.00472098936395306, 0.00703993721171044)
(4.3090029815474855, 0.228716858577315)
(-64.2415909824392, 4.61837802533875e-5)
(-99.85155728360215, 1.98667557656896e-5)
(16.352480952156846, 0.00093820720267014)
(54.07472774983936, 2.30320717123636e-5)
(76.0642797634986, 4.0520054563236e-5)
(-97.75698930723041, 2.06961481855626e-5)
(-65.30611519274892, 1.76383760878553e-5)
(78.15884319104435, 3.8275083834777e-5)
(-49.574393748197714, 7.51524099290489e-5)
(71.87512463251068, 4.56457650249106e-5)
(62.453290644331894, 1.46356475537861e-5)
(-5.597465898899744, 0.00250310429799629)
(-46.46857535427074, 4.76620538937431e-5)
(6.838440247470991, 0.0199073873216171)
(-20.294118058301148, 0.000372510205574181)
(-84.15269787981894, 8.50580277543236e-6)
(-16.091222280404757, 0.000548059488815053)
(34.16881779684687, 0.000227763012058026)
(49.885291707159986, 2.96454519368826e-5)
(-23.269421251652275, 0.000376545212199885)
(42.54909915710838, 0.000140284825348392)
(-3.498139865533535, 0.754192471752606)
(-71.58793540163579, 1.35280599060176e-5)
(88.63154531781782, 2.94265184455595e-5)
(25.786661484172907, 0.000432403703654759)
(91.77662357902187, 4.26314417245259e-6)
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:
$$x_{1} = -24.5240066237629$$
$$x_{2} = -33.9676954985314$$
$$x_{3} = -13.9920612178121$$
$$x_{4} = -38.114982279046$$
$$x_{5} = -18.1915200799956$$
$$x_{6} = -30.0321420491974$$
$$x_{7} = -90.435387981693$$
$$x_{8} = -86.246911706429$$
$$x_{9} = -82.0585032601189$$
$$x_{10} = -40.1999226246919$$
$$x_{11} = -73.6819803901426$$
$$x_{12} = -7.69628941684326$$
$$x_{13} = -75.7760648726363$$
$$x_{14} = -69.4939368365511$$
$$x_{15} = -77.8701831725522$$
$$x_{16} = -36.035537667834$$
$$x_{17} = -42.2878728663535$$
$$x_{18} = -79.9643306018706$$
$$x_{19} = -31.9311177846054$$
$$x_{20} = -11.8934260810529$$
$$x_{21} = -9.79492708855456$$
$$x_{22} = -1.43269912489468$$
$$x_{23} = -65.3061151927489$$
$$x_{24} = -5.59746589889974$$
$$x_{25} = -46.4685753542707$$
$$x_{26} = -20.2941180583011$$
$$x_{27} = -84.1526978798189$$
$$x_{28} = -16.0912222804048$$
$$x_{29} = -71.5879354016358$$
Puntos máximos de la función:
$$x_{29} = -25.2891830586486$$
$$x_{29} = 10.0413977591473$$
$$x_{29} = -51.6701521437033$$
$$x_{29} = -57.9563573415376$$
$$x_{29} = 81.30418750723$$
$$x_{29} = -93.5678237386056$$
$$x_{29} = 56.1694022547987$$
$$x_{29} = 38.3591097543705$$
$$x_{29} = 51.980025552783$$
$$x_{29} = 82.3479453186041$$
$$x_{29} = 84.4424852259481$$
$$x_{29} = 40.4541360154989$$
$$x_{29} = -95.6624117412458$$
$$x_{29} = 70.8315760569921$$
$$x_{29} = 36.2640086520819$$
$$x_{29} = -60.0515160044936$$
$$x_{29} = 12.1491641598531$$
$$x_{29} = 86.5370184030478$$
$$x_{29} = 27.8824805114201$$
$$x_{29} = 60.3586810642082$$
$$x_{29} = 7.9231607457098$$
$$x_{29} = -55.8610947638737$$
$$x_{29} = -91.4732243467267$$
$$x_{29} = 2.55352749832256$$
$$x_{29} = 44.6440085282705$$
$$x_{29} = 64.5478832428738$$
$$x_{29} = -43.2850467361486$$
$$x_{29} = 69.7805312521359$$
$$x_{29} = 32.0735179028996$$
$$x_{29} = 93.8710955963389$$
$$x_{29} = 95.9655634340815$$
$$x_{29} = 100.154487776243$$
$$x_{29} = 29.97808355276$$
$$x_{29} = 80.2533981643314$$
$$x_{29} = 14.252130607825$$
$$x_{29} = 73.969707174174$$
$$x_{29} = -53.7657039727558$$
$$x_{29} = 20.5489679565243$$
$$x_{29} = -47.4783636242956$$
$$x_{29} = 58.2640524116865$$
$$x_{29} = 98.0600274007149$$
$$x_{29} = -62.1465891503376$$
$$x_{29} = 99.104099575324$$
$$x_{29} = 18.4512432534799$$
$$x_{29} = 0.00472098936395306$$
$$x_{29} = 4.30900298154749$$
$$x_{29} = -64.2415909824392$$
$$x_{29} = -99.8515572836021$$
$$x_{29} = 16.3524809521568$$
$$x_{29} = 54.0747277498394$$
$$x_{29} = 76.0642797634986$$
$$x_{29} = -97.7569893072304$$
$$x_{29} = 78.1588431910444$$
$$x_{29} = -49.5743937481977$$
$$x_{29} = 71.8751246325107$$
$$x_{29} = 62.4532906443319$$
$$x_{29} = 6.83844024747099$$
$$x_{29} = 34.1688177968469$$
$$x_{29} = 49.88529170716$$
$$x_{29} = -23.2694212516523$$
$$x_{29} = 42.5490991571084$$
$$x_{29} = -3.49813986553354$$
$$x_{29} = 88.6315453178178$$
$$x_{29} = 25.7866614841729$$
$$x_{29} = 91.7766235790219$$
Decrece en los intervalos
$$\left[-1.43269912489468, \infty\right)$$
Crece en los intervalos
$$\left(-\infty, -90.435387981693\right]$$
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:
$$\left|{\left(- \frac{3 \operatorname{sinc}^{2}{\left(\frac{3 \left(x - \frac{7}{2}\right)}{2} \right)}}{4} - \frac{3 \operatorname{sinc}^{2}{\left(\frac{3 \left(x + \frac{7}{2}\right)}{2} \right)}}{4}\right) + \operatorname{sinc}^{2}{\left(\frac{3 \left(x - 3\right)}{2} \right)}}\right| = \left|{\frac{3 \operatorname{sinc}^{2}{\left(\frac{3 x}{2} - \frac{21}{4} \right)}}{4} - \operatorname{sinc}^{2}{\left(\frac{3 x}{2} + \frac{9}{2} \right)} + \frac{3 \operatorname{sinc}^{2}{\left(\frac{3 x}{2} + \frac{21}{4} \right)}}{4}}\right|$$
- No
$$\left|{\left(- \frac{3 \operatorname{sinc}^{2}{\left(\frac{3 \left(x - \frac{7}{2}\right)}{2} \right)}}{4} - \frac{3 \operatorname{sinc}^{2}{\left(\frac{3 \left(x + \frac{7}{2}\right)}{2} \right)}}{4}\right) + \operatorname{sinc}^{2}{\left(\frac{3 \left(x - 3\right)}{2} \right)}}\right| = - \left|{\frac{3 \operatorname{sinc}^{2}{\left(\frac{3 x}{2} - \frac{21}{4} \right)}}{4} - \operatorname{sinc}^{2}{\left(\frac{3 x}{2} + \frac{9}{2} \right)} + \frac{3 \operatorname{sinc}^{2}{\left(\frac{3 x}{2} + \frac{21}{4} \right)}}{4}}\right|$$
- No
es decir, función
no es
par ni impar
Pues, comprobamos:
$$\left|{\left(- \frac{3 \operatorname{sinc}^{2}{\left(\frac{3 \left(x - \frac{7}{2}\right)}{2} \right)}}{4} - \frac{3 \operatorname{sinc}^{2}{\left(\frac{3 \left(x + \frac{7}{2}\right)}{2} \right)}}{4}\right) + \operatorname{sinc}^{2}{\left(\frac{3 \left(x - 3\right)}{2} \right)}}\right| = \left|{\frac{3 \operatorname{sinc}^{2}{\left(\frac{3 x}{2} - \frac{21}{4} \right)}}{4} - \operatorname{sinc}^{2}{\left(\frac{3 x}{2} + \frac{9}{2} \right)} + \frac{3 \operatorname{sinc}^{2}{\left(\frac{3 x}{2} + \frac{21}{4} \right)}}{4}}\right|$$
- No
$$\left|{\left(- \frac{3 \operatorname{sinc}^{2}{\left(\frac{3 \left(x - \frac{7}{2}\right)}{2} \right)}}{4} - \frac{3 \operatorname{sinc}^{2}{\left(\frac{3 \left(x + \frac{7}{2}\right)}{2} \right)}}{4}\right) + \operatorname{sinc}^{2}{\left(\frac{3 \left(x - 3\right)}{2} \right)}}\right| = - \left|{\frac{3 \operatorname{sinc}^{2}{\left(\frac{3 x}{2} - \frac{21}{4} \right)}}{4} - \operatorname{sinc}^{2}{\left(\frac{3 x}{2} + \frac{9}{2} \right)} + \frac{3 \operatorname{sinc}^{2}{\left(\frac{3 x}{2} + \frac{21}{4} \right)}}{4}}\right|$$
- No
es decir, función
no es
par ni impar