Sr Examen
Otras calculadoras
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- Derivadas paso a paso
- Integrales paso a paso
- Gráfico de la función paramétrica
- Gráfico en coordenadas polares
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- 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/(1+x^2)
-
y^2+1
-
x/(x-1)
-
x/(x^2-1)
-
Expresiones idénticas
- dos *cos(tres *x)- siete *cos(dos *x)* tres *x- siete *cos(dos *x)- catorce *cos(x)
- 2 multiplicar por coseno de (3 multiplicar por x) menos 7 multiplicar por coseno de (2 multiplicar por x) multiplicar por 3 multiplicar por x menos 7 multiplicar por coseno de (2 multiplicar por x) menos 14 multiplicar por coseno de (x)
- dos multiplicar por coseno de (tres multiplicar por x) menos siete multiplicar por coseno de (dos multiplicar por x) multiplicar por tres multiplicar por x menos siete multiplicar por coseno de (dos multiplicar por x) menos cotangente de angente de orce multiplicar por coseno de (x)
- 2cos(3x)-7cos(2x)3x-7cos(2x)-14cos(x)
- 2cos3x-7cos2x3x-7cos2x-14cosx
-
Expresiones semejantes
- 2*cos(3*x)+7*cos(2*x)*3*x-7*cos(2*x)-14*cos(x)
- 2*cos(3*x)-7*cos(2*x)*3*x+7*cos(2*x)-14*cos(x)
- 2*cos(3*x)-7*cos(2*x)*3*x-7*cos(2*x)+14*cos(x)
- 2*cos(3*x)-7*cos(2*x)*3*x-7*cos(2*x)-14*cosx
-
Expresiones con funciones
- Coseno cos
- cos(x)-sin(x)
- cos(x+1)
- cos(x)+x
- cos(x)+2
- cosx+1/2sin2x
- Coseno cos
- cos(x)-sin(x)
- cos(x+1)
- cos(x)+x
- cos(x)+2
- cosx+1/2sin2x
- Coseno cos
- cos(x)-sin(x)
- cos(x+1)
- cos(x)+x
- cos(x)+2
- cosx+1/2sin2x
- Coseno cos
- cos(x)-sin(x)
- cos(x+1)
- cos(x)+x
- cos(x)+2
- cosx+1/2sin2x
Gráfico de la función y = 2*cos(3*x)-7*cos(2*x)*3*x-7*cos(2*x)-14*cos(x)
Solución
Ha introducido
[src]
f(x) = 2*cos(3*x) - 7*cos(2*x)*3*x - 7*cos(2*x) - 14*cos(x)
$$f{\left(x \right)} = \left(\left(- x 3 \cdot 7 \cos{\left(2 x \right)} + 2 \cos{\left(3 x \right)}\right) - 7 \cos{\left(2 x \right)}\right) - 14 \cos{\left(x \right)}$$
f = -x*3*(7*cos(2*x)) + 2*cos(3*x) - 7*cos(2*x) - 14*cos(x)
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:
$$\left(\left(- x 3 \cdot 7 \cos{\left(2 x \right)} + 2 \cos{\left(3 x \right)}\right) - 7 \cos{\left(2 x \right)}\right) - 14 \cos{\left(x \right)} = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución numérica
$$x_{1} = -79.3286186868585$$
$$x_{2} = 0.96976315786421$$
$$x_{3} = -33.7640958654435$$
$$x_{4} = -13.330829611389$$
$$x_{5} = 33.7800485957099$$
$$x_{6} = 54.1875203268219$$
$$x_{7} = 91.8886599233614$$
$$x_{8} = 19.6483440506237$$
$$x_{9} = 47.9036880055106$$
$$x_{10} = -93.4652780164121$$
$$x_{11} = -32.1928339429512$$
$$x_{12} = 96.6067567248107$$
$$x_{13} = -82.4635219393152$$
$$x_{14} = -90.3177997124238$$
$$x_{15} = 46.3442792234221$$
$$x_{16} = -11.8047294380989$$
$$x_{17} = 68.3257245598241$$
$$x_{18} = -76.1800639891199$$
$$x_{19} = 66.7548206083775$$
$$x_{20} = 5.45232194697703$$
$$x_{21} = -47.9149332328647$$
$$x_{22} = 82.4700550384384$$
$$x_{23} = -18.0794520134705$$
$$x_{24} = 13.3712307064103$$
$$x_{25} = 27.4986610579683$$
$$x_{26} = -16.5098745115795$$
$$x_{27} = 24.3364836195886$$
$$x_{28} = 99.7428786869862$$
$$x_{29} = -40.0485467217252$$
$$x_{30} = 30.6218642316085$$
$$x_{31} = -10.237003770154$$
$$x_{32} = 73.0383510985983$$
$$x_{33} = 25.9283439961946$$
$$x_{34} = 90.323764553498$$
$$x_{35} = 77.7578736018635$$
$$x_{36} = 76.1871359366327$$
$$x_{37} = -84.0343903781717$$
$$x_{38} = -85.6115535855662$$
$$x_{39} = -35.3505803351934$$
$$x_{40} = 60.4712186135938$$
$$x_{41} = -5.55074154552555$$
$$x_{42} = 10.1842375562936$$
$$x_{43} = -71.4674531971057$$
$$x_{44} = -91.8945227984772$$
$$x_{45} = -62.0508290562559$$
$$x_{46} = -60.4801271546578$$
$$x_{47} = 41.6196612147716$$
$$x_{48} = 85.6052604062619$$
$$x_{49} = 11.7589450481684$$
$$x_{50} = -27.4790617833793$$
$$x_{51} = -77.7509447406708$$
$$x_{52} = -41.6326038532267$$
$$x_{53} = 69.9042643658696$$
$$x_{54} = 16.4772092502488$$
$$x_{55} = 14.9403566810386$$
$$x_{56} = 63.6214543030474$$
$$x_{57} = 74.6092375807615$$
$$x_{58} = 38.4914241105263$$
$$x_{59} = 2.4573496807162$$
$$x_{60} = -63.612985298967$$
$$x_{61} = 49.4746906867931$$
$$x_{62} = 98.1720320747266$$
$$x_{63} = -19.6208905627261$$
$$x_{64} = -49.4855796988963$$
$$x_{65} = 62.042145652071$$
$$x_{66} = -55.7681406919688$$
$$x_{67} = -24.3586179146243$$
$$x_{68} = 52.6267762292029$$
$$x_{69} = -69.8965566871116$$
$$x_{70} = -25.9075509819384$$
$$x_{71} = 84.0408011908752$$
$$x_{72} = 8.66974571901423$$
$$x_{73} = 40.0619969877346$$
$$x_{74} = -2.22420547332476$$
$$x_{75} = 18.0496119247806$$
$$x_{76} = -38.4774230870637$$
$$x_{77} = 32.209567896301$$
$$x_{78} = -57.3293285762611$$
$$x_{79} = -3.99775823441916$$
$$x_{80} = -46.332652760818$$
$$x_{81} = 55.7584787653484$$
$$x_{82} = -68.3336094231474$$
$$x_{83} = -54.1974617496389$$
$$x_{84} = -99.7482800134655$$
$$x_{85} = 3.86071461784559$$
$$x_{86} = 88.7530116308266$$
$$x_{87} = -98.1775197248071$$
o sea hay que resolver la ecuación:
$$\left(\left(- x 3 \cdot 7 \cos{\left(2 x \right)} + 2 \cos{\left(3 x \right)}\right) - 7 \cos{\left(2 x \right)}\right) - 14 \cos{\left(x \right)} = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución numérica
$$x_{1} = -79.3286186868585$$
$$x_{2} = 0.96976315786421$$
$$x_{3} = -33.7640958654435$$
$$x_{4} = -13.330829611389$$
$$x_{5} = 33.7800485957099$$
$$x_{6} = 54.1875203268219$$
$$x_{7} = 91.8886599233614$$
$$x_{8} = 19.6483440506237$$
$$x_{9} = 47.9036880055106$$
$$x_{10} = -93.4652780164121$$
$$x_{11} = -32.1928339429512$$
$$x_{12} = 96.6067567248107$$
$$x_{13} = -82.4635219393152$$
$$x_{14} = -90.3177997124238$$
$$x_{15} = 46.3442792234221$$
$$x_{16} = -11.8047294380989$$
$$x_{17} = 68.3257245598241$$
$$x_{18} = -76.1800639891199$$
$$x_{19} = 66.7548206083775$$
$$x_{20} = 5.45232194697703$$
$$x_{21} = -47.9149332328647$$
$$x_{22} = 82.4700550384384$$
$$x_{23} = -18.0794520134705$$
$$x_{24} = 13.3712307064103$$
$$x_{25} = 27.4986610579683$$
$$x_{26} = -16.5098745115795$$
$$x_{27} = 24.3364836195886$$
$$x_{28} = 99.7428786869862$$
$$x_{29} = -40.0485467217252$$
$$x_{30} = 30.6218642316085$$
$$x_{31} = -10.237003770154$$
$$x_{32} = 73.0383510985983$$
$$x_{33} = 25.9283439961946$$
$$x_{34} = 90.323764553498$$
$$x_{35} = 77.7578736018635$$
$$x_{36} = 76.1871359366327$$
$$x_{37} = -84.0343903781717$$
$$x_{38} = -85.6115535855662$$
$$x_{39} = -35.3505803351934$$
$$x_{40} = 60.4712186135938$$
$$x_{41} = -5.55074154552555$$
$$x_{42} = 10.1842375562936$$
$$x_{43} = -71.4674531971057$$
$$x_{44} = -91.8945227984772$$
$$x_{45} = -62.0508290562559$$
$$x_{46} = -60.4801271546578$$
$$x_{47} = 41.6196612147716$$
$$x_{48} = 85.6052604062619$$
$$x_{49} = 11.7589450481684$$
$$x_{50} = -27.4790617833793$$
$$x_{51} = -77.7509447406708$$
$$x_{52} = -41.6326038532267$$
$$x_{53} = 69.9042643658696$$
$$x_{54} = 16.4772092502488$$
$$x_{55} = 14.9403566810386$$
$$x_{56} = 63.6214543030474$$
$$x_{57} = 74.6092375807615$$
$$x_{58} = 38.4914241105263$$
$$x_{59} = 2.4573496807162$$
$$x_{60} = -63.612985298967$$
$$x_{61} = 49.4746906867931$$
$$x_{62} = 98.1720320747266$$
$$x_{63} = -19.6208905627261$$
$$x_{64} = -49.4855796988963$$
$$x_{65} = 62.042145652071$$
$$x_{66} = -55.7681406919688$$
$$x_{67} = -24.3586179146243$$
$$x_{68} = 52.6267762292029$$
$$x_{69} = -69.8965566871116$$
$$x_{70} = -25.9075509819384$$
$$x_{71} = 84.0408011908752$$
$$x_{72} = 8.66974571901423$$
$$x_{73} = 40.0619969877346$$
$$x_{74} = -2.22420547332476$$
$$x_{75} = 18.0496119247806$$
$$x_{76} = -38.4774230870637$$
$$x_{77} = 32.209567896301$$
$$x_{78} = -57.3293285762611$$
$$x_{79} = -3.99775823441916$$
$$x_{80} = -46.332652760818$$
$$x_{81} = 55.7584787653484$$
$$x_{82} = -68.3336094231474$$
$$x_{83} = -54.1974617496389$$
$$x_{84} = -99.7482800134655$$
$$x_{85} = 3.86071461784559$$
$$x_{86} = 88.7530116308266$$
$$x_{87} = -98.1775197248071$$
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
$$42 x \sin{\left(2 x \right)} + 14 \sin{\left(x \right)} + 14 \sin{\left(2 x \right)} - 6 \sin{\left(3 x \right)} - 21 \cos{\left(2 x \right)} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = -51.8365099303089$$
$$x_{2} = -7.85556421545038$$
$$x_{3} = 95.8236518040196$$
$$x_{4} = -86.399468922026$$
$$x_{5} = -94.2504401555016$$
$$x_{6} = -42.4230955040777$$
$$x_{7} = -83.2523488910586$$
$$x_{8} = -89.5355240854703$$
$$x_{9} = 0.329878181493422$$
$$x_{10} = -54.9868013201444$$
$$x_{11} = -95.8187006107704$$
$$x_{12} = 72.2600725597578$$
$$x_{13} = 64.4101877947986$$
$$x_{14} = -1.58033665004861$$
$$x_{15} = 22.0023157913067$$
$$x_{16} = 48.6949289448107$$
$$x_{17} = 50.2704272932174$$
$$x_{18} = 6.32095174977373$$
$$x_{19} = -15.7242511883627$$
$$x_{20} = -20.4209448887882$$
$$x_{21} = -58.119670104785$$
$$x_{22} = 100.533444581925$$
$$x_{23} = 43.9879436077029$$
$$x_{24} = -39.2702139148003$$
$$x_{25} = -73.8340676969796$$
$$x_{26} = -37.7057923529646$$
$$x_{27} = -97.391949265849$$
$$x_{28} = 86.3939352403536$$
$$x_{29} = 51.8456320657499$$
$$x_{30} = 87.9674270304944$$
$$x_{31} = -67.5515029564298$$
$$x_{32} = 58.1278124542836$$
$$x_{33} = 1.78796740242292$$
$$x_{34} = 67.5444174374737$$
$$x_{35} = -31.4239545634883$$
$$x_{36} = -0.589149345698636$$
$$x_{37} = 56.5530660562027$$
$$x_{38} = 37.7056918967783$$
$$x_{39} = -59.6944752084758$$
$$x_{40} = -72.2601090360426$$
$$x_{41} = -23.5829276401346$$
$$x_{42} = 26.7215715058841$$
$$x_{43} = -22.0027089238939$$
$$x_{44} = 59.6944217613547$$
$$x_{45} = 28.2830547433159$$
$$x_{46} = -12.5866832131152$$
$$x_{47} = 42.4117793291063$$
$$x_{48} = 7.91292734920106$$
$$x_{49} = 73.8275878854089$$
$$x_{50} = 45.5637266141872$$
$$x_{51} = -80.1167301493193$$
$$x_{52} = 80.1107606545324$$
$$x_{53} = -36.1419431785463$$
$$x_{54} = -43.9880174241053$$
$$x_{55} = -65.9772568416673$$
$$x_{56} = -17.3074866297774$$
$$x_{57} = -28.2832927385975$$
$$x_{58} = 20.4438287899401$$
$$x_{59} = 89.5408213115049$$
$$x_{60} = -75.4015518300676$$
$$x_{61} = -9.45230877575799$$
$$x_{62} = -102.101878220453$$
$$x_{63} = 70.6927063810377$$
$$x_{64} = 81.6844588452805$$
$$x_{65} = -14.1380293069029$$
$$x_{66} = -29.8616545835409$$
$$x_{67} = 23.5624430962496$$
$$x_{68} = 34.5646726754472$$
$$x_{69} = 29.8455246822244$$
$$x_{70} = -50.2704838147943$$
$$x_{71} = 65.9772130881693$$
$$x_{72} = 92.6771112747014$$
$$x_{73} = -81.6844802544329$$
$$x_{74} = -87.9674454907549$$
$$x_{75} = -45.5533567399819$$
$$x_{76} = -53.4117892090852$$
$$x_{77} = 78.5429839043088$$
$$x_{78} = -3.22844409727052$$
$$x_{79} = 94.2504240743329$$
$$x_{80} = 12.5857834640896$$
$$x_{81} = -6.32449323163835$$
$$x_{82} = 14.1707740307198$$
$$x_{83} = 15.723482018271$$
$$x_{84} = -61.2690661353708$$
$$x_{85} = 36.128642014024$$
$$x_{86} = -64.4028352086649$$
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:
$$x_{1} = -51.8365099303089$$
$$x_{2} = -7.85556421545038$$
$$x_{3} = -86.399468922026$$
$$x_{4} = -42.4230955040777$$
$$x_{5} = -83.2523488910586$$
$$x_{6} = -89.5355240854703$$
$$x_{7} = 0.329878181493422$$
$$x_{8} = -54.9868013201444$$
$$x_{9} = -95.8187006107704$$
$$x_{10} = 72.2600725597578$$
$$x_{11} = -1.58033665004861$$
$$x_{12} = 22.0023157913067$$
$$x_{13} = 50.2704272932174$$
$$x_{14} = 6.32095174977373$$
$$x_{15} = -20.4209448887882$$
$$x_{16} = -58.119670104785$$
$$x_{17} = 100.533444581925$$
$$x_{18} = 43.9879436077029$$
$$x_{19} = -39.2702139148003$$
$$x_{20} = -73.8340676969796$$
$$x_{21} = 87.9674270304944$$
$$x_{22} = -67.5515029564298$$
$$x_{23} = 56.5530660562027$$
$$x_{24} = 37.7056918967783$$
$$x_{25} = -23.5829276401346$$
$$x_{26} = 59.6944217613547$$
$$x_{27} = 28.2830547433159$$
$$x_{28} = -80.1167301493193$$
$$x_{29} = -36.1419431785463$$
$$x_{30} = -17.3074866297774$$
$$x_{31} = -102.101878220453$$
$$x_{32} = 81.6844588452805$$
$$x_{33} = -14.1380293069029$$
$$x_{34} = -29.8616545835409$$
$$x_{35} = 34.5646726754472$$
$$x_{36} = 65.9772130881693$$
$$x_{37} = -45.5533567399819$$
$$x_{38} = 78.5429839043088$$
$$x_{39} = 94.2504240743329$$
$$x_{40} = 12.5857834640896$$
$$x_{41} = 15.723482018271$$
$$x_{42} = -61.2690661353708$$
$$x_{43} = -64.4028352086649$$
Puntos máximos de la función:
$$x_{43} = 95.8236518040196$$
$$x_{43} = -94.2504401555016$$
$$x_{43} = 64.4101877947986$$
$$x_{43} = 48.6949289448107$$
$$x_{43} = -15.7242511883627$$
$$x_{43} = -37.7057923529646$$
$$x_{43} = -97.391949265849$$
$$x_{43} = 86.3939352403536$$
$$x_{43} = 51.8456320657499$$
$$x_{43} = 58.1278124542836$$
$$x_{43} = 1.78796740242292$$
$$x_{43} = 67.5444174374737$$
$$x_{43} = -31.4239545634883$$
$$x_{43} = -0.589149345698636$$
$$x_{43} = -59.6944752084758$$
$$x_{43} = -72.2601090360426$$
$$x_{43} = 26.7215715058841$$
$$x_{43} = -22.0027089238939$$
$$x_{43} = -12.5866832131152$$
$$x_{43} = 42.4117793291063$$
$$x_{43} = 7.91292734920106$$
$$x_{43} = 73.8275878854089$$
$$x_{43} = 45.5637266141872$$
$$x_{43} = 80.1107606545324$$
$$x_{43} = -43.9880174241053$$
$$x_{43} = -65.9772568416673$$
$$x_{43} = -28.2832927385975$$
$$x_{43} = 20.4438287899401$$
$$x_{43} = 89.5408213115049$$
$$x_{43} = -75.4015518300676$$
$$x_{43} = -9.45230877575799$$
$$x_{43} = 70.6927063810377$$
$$x_{43} = 23.5624430962496$$
$$x_{43} = 29.8455246822244$$
$$x_{43} = -50.2704838147943$$
$$x_{43} = 92.6771112747014$$
$$x_{43} = -81.6844802544329$$
$$x_{43} = -87.9674454907549$$
$$x_{43} = -53.4117892090852$$
$$x_{43} = -3.22844409727052$$
$$x_{43} = -6.32449323163835$$
$$x_{43} = 14.1707740307198$$
$$x_{43} = 36.128642014024$$
Decrece en los intervalos
$$\left[100.533444581925, \infty\right)$$
Crece en los intervalos
$$\left(-\infty, -102.101878220453\right]$$
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(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
$$42 x \sin{\left(2 x \right)} + 14 \sin{\left(x \right)} + 14 \sin{\left(2 x \right)} - 6 \sin{\left(3 x \right)} - 21 \cos{\left(2 x \right)} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = -51.8365099303089$$
$$x_{2} = -7.85556421545038$$
$$x_{3} = 95.8236518040196$$
$$x_{4} = -86.399468922026$$
$$x_{5} = -94.2504401555016$$
$$x_{6} = -42.4230955040777$$
$$x_{7} = -83.2523488910586$$
$$x_{8} = -89.5355240854703$$
$$x_{9} = 0.329878181493422$$
$$x_{10} = -54.9868013201444$$
$$x_{11} = -95.8187006107704$$
$$x_{12} = 72.2600725597578$$
$$x_{13} = 64.4101877947986$$
$$x_{14} = -1.58033665004861$$
$$x_{15} = 22.0023157913067$$
$$x_{16} = 48.6949289448107$$
$$x_{17} = 50.2704272932174$$
$$x_{18} = 6.32095174977373$$
$$x_{19} = -15.7242511883627$$
$$x_{20} = -20.4209448887882$$
$$x_{21} = -58.119670104785$$
$$x_{22} = 100.533444581925$$
$$x_{23} = 43.9879436077029$$
$$x_{24} = -39.2702139148003$$
$$x_{25} = -73.8340676969796$$
$$x_{26} = -37.7057923529646$$
$$x_{27} = -97.391949265849$$
$$x_{28} = 86.3939352403536$$
$$x_{29} = 51.8456320657499$$
$$x_{30} = 87.9674270304944$$
$$x_{31} = -67.5515029564298$$
$$x_{32} = 58.1278124542836$$
$$x_{33} = 1.78796740242292$$
$$x_{34} = 67.5444174374737$$
$$x_{35} = -31.4239545634883$$
$$x_{36} = -0.589149345698636$$
$$x_{37} = 56.5530660562027$$
$$x_{38} = 37.7056918967783$$
$$x_{39} = -59.6944752084758$$
$$x_{40} = -72.2601090360426$$
$$x_{41} = -23.5829276401346$$
$$x_{42} = 26.7215715058841$$
$$x_{43} = -22.0027089238939$$
$$x_{44} = 59.6944217613547$$
$$x_{45} = 28.2830547433159$$
$$x_{46} = -12.5866832131152$$
$$x_{47} = 42.4117793291063$$
$$x_{48} = 7.91292734920106$$
$$x_{49} = 73.8275878854089$$
$$x_{50} = 45.5637266141872$$
$$x_{51} = -80.1167301493193$$
$$x_{52} = 80.1107606545324$$
$$x_{53} = -36.1419431785463$$
$$x_{54} = -43.9880174241053$$
$$x_{55} = -65.9772568416673$$
$$x_{56} = -17.3074866297774$$
$$x_{57} = -28.2832927385975$$
$$x_{58} = 20.4438287899401$$
$$x_{59} = 89.5408213115049$$
$$x_{60} = -75.4015518300676$$
$$x_{61} = -9.45230877575799$$
$$x_{62} = -102.101878220453$$
$$x_{63} = 70.6927063810377$$
$$x_{64} = 81.6844588452805$$
$$x_{65} = -14.1380293069029$$
$$x_{66} = -29.8616545835409$$
$$x_{67} = 23.5624430962496$$
$$x_{68} = 34.5646726754472$$
$$x_{69} = 29.8455246822244$$
$$x_{70} = -50.2704838147943$$
$$x_{71} = 65.9772130881693$$
$$x_{72} = 92.6771112747014$$
$$x_{73} = -81.6844802544329$$
$$x_{74} = -87.9674454907549$$
$$x_{75} = -45.5533567399819$$
$$x_{76} = -53.4117892090852$$
$$x_{77} = 78.5429839043088$$
$$x_{78} = -3.22844409727052$$
$$x_{79} = 94.2504240743329$$
$$x_{80} = 12.5857834640896$$
$$x_{81} = -6.32449323163835$$
$$x_{82} = 14.1707740307198$$
$$x_{83} = 15.723482018271$$
$$x_{84} = -61.2690661353708$$
$$x_{85} = 36.128642014024$$
$$x_{86} = -64.4028352086649$$
Signos de extremos en los puntos:
(-51.836509930308914, -1081.56197004209)
(-7.8555642154503795, -157.934405664318)
(95.82365180401965, 2019.29415254338)
(-86.39946892202596, -1807.38601550549)
(-94.2504401555016, 1960.23130784285)
(-42.42309550407768, -883.87923915983)
(-83.25234889105865, -1741.29638350823)
(-89.53552408547027, -1873.24326990261)
(0.32987818149342163, -23.1518056066285)
(-54.986801320144444, -1147.71837690488)
(-95.81870061077038, -2005.19015696243)
(72.26007255975777, -1512.42538843195)
(64.41018779479862, 1359.61018298894)
(-1.5803366500486136, -25.9915061941676)
(22.002315791306742, -456.931400132763)
(48.69492894481069, 1029.58853015078)
(50.27042729321739, -1074.62705450104)
(6.320951749773726, -151.344392841563)
(-15.72425118836271, 335.038327796469)
(-20.420944888788178, -421.827693538391)
(-58.119670104785, -1213.50884892645)
(100.53344458192505, -2130.17629998341)
(43.98794360770294, -942.687531114567)
(-39.27021391480026, -817.668224440218)
(-73.83406769697959, -1543.51210727491)
(-37.70579235296464, 772.751499265023)
(-97.39194926584895, 2050.20387633462)
(86.39393524035363, 1821.26982608146)
(51.84563206574991, 1095.7536129686)
(87.96742703049442, -1866.28622437373)
(-67.5515029564298, -1411.57793922504)
(58.12781245428362, 1227.67989889822)
(1.7879674024229206, 44.6402996273095)
(67.54441743747374, 1425.42917078852)
(-31.423954563488316, 640.818760575166)
(-0.5891493456986355, -9.97573676148234)
(56.55306605620269, -1206.56820660964)
(37.705691896778276, -810.750444264482)
(-59.694475208475794, 1258.53972539218)
(-72.26010903604264, 1522.42577145744)
(-23.582927640134553, -488.231172284164)
(26.72157150588405, 568.144100965784)
(-22.002708923893866, 466.935530874201)
(59.69442176135469, -1248.53916414481)
(28.283054743315944, -588.852592144067)
(-12.58668321311524, 245.107210915045)
(42.41177932910629, 897.641656545856)
(7.912927349201056, 173.146061235533)
(73.82758788540889, 1557.37605480965)
(45.56372661418715, 963.832966172958)
(-80.11673014931932, -1675.4482789349)
(80.11076065453241, 1689.32293999138)
(-36.141943178546256, -751.974043111704)
(-43.98801742410533, 904.68830630049)
(-65.97725684166733, 1390.48237792393)
(-17.307486629777394, -356.443325827242)
(-28.283292738597506, 598.855092138194)
(20.443828789940113, 436.308922918765)
(89.54082131150487, 1887.35453537607)
(-75.40155183006765, 1564.39764356479)
(-9.45230877575799, 203.209779041118)
(-102.10187822045306, -2137.13704456445)
(70.69270638103765, 1491.54340459963)
(81.68445884528053, -1734.34161280238)
(-14.138029306902906, -289.880936956837)
(-29.861654583540886, -620.086573552288)
(23.562443096249623, 501.801092039431)
(34.564672675447234, -720.783020973452)
(29.845524682224376, 633.747931628655)
(-50.27048381479426, 1036.62764804426)
(65.9772130881693, -1380.48191847695)
(92.67711127470137, 1953.21671289581)
(-81.68448025443287, 1696.34183760805)
(-87.96744549075494, 1828.28641821358)
(-45.55335673998194, -949.615094649834)
(-53.411789209085235, 1126.59807719719)
(78.5429839043088, -1644.36940311819)
(-3.22844409727052, 71.8971567448386)
(94.25042407433291, -1998.23113898518)
(12.58578346408958, -283.097746629252)
(-6.324493231638353, 113.381841973545)
(14.170774030719816, 304.570203773481)
(15.723482018270955, -325.030240589651)
(-61.269066135370764, -1279.64639433796)
(36.12864201402404, 765.694789091334)
(-64.40283520866485, -1345.45573027554)
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:
$$x_{1} = -51.8365099303089$$
$$x_{2} = -7.85556421545038$$
$$x_{3} = -86.399468922026$$
$$x_{4} = -42.4230955040777$$
$$x_{5} = -83.2523488910586$$
$$x_{6} = -89.5355240854703$$
$$x_{7} = 0.329878181493422$$
$$x_{8} = -54.9868013201444$$
$$x_{9} = -95.8187006107704$$
$$x_{10} = 72.2600725597578$$
$$x_{11} = -1.58033665004861$$
$$x_{12} = 22.0023157913067$$
$$x_{13} = 50.2704272932174$$
$$x_{14} = 6.32095174977373$$
$$x_{15} = -20.4209448887882$$
$$x_{16} = -58.119670104785$$
$$x_{17} = 100.533444581925$$
$$x_{18} = 43.9879436077029$$
$$x_{19} = -39.2702139148003$$
$$x_{20} = -73.8340676969796$$
$$x_{21} = 87.9674270304944$$
$$x_{22} = -67.5515029564298$$
$$x_{23} = 56.5530660562027$$
$$x_{24} = 37.7056918967783$$
$$x_{25} = -23.5829276401346$$
$$x_{26} = 59.6944217613547$$
$$x_{27} = 28.2830547433159$$
$$x_{28} = -80.1167301493193$$
$$x_{29} = -36.1419431785463$$
$$x_{30} = -17.3074866297774$$
$$x_{31} = -102.101878220453$$
$$x_{32} = 81.6844588452805$$
$$x_{33} = -14.1380293069029$$
$$x_{34} = -29.8616545835409$$
$$x_{35} = 34.5646726754472$$
$$x_{36} = 65.9772130881693$$
$$x_{37} = -45.5533567399819$$
$$x_{38} = 78.5429839043088$$
$$x_{39} = 94.2504240743329$$
$$x_{40} = 12.5857834640896$$
$$x_{41} = 15.723482018271$$
$$x_{42} = -61.2690661353708$$
$$x_{43} = -64.4028352086649$$
Puntos máximos de la función:
$$x_{43} = 95.8236518040196$$
$$x_{43} = -94.2504401555016$$
$$x_{43} = 64.4101877947986$$
$$x_{43} = 48.6949289448107$$
$$x_{43} = -15.7242511883627$$
$$x_{43} = -37.7057923529646$$
$$x_{43} = -97.391949265849$$
$$x_{43} = 86.3939352403536$$
$$x_{43} = 51.8456320657499$$
$$x_{43} = 58.1278124542836$$
$$x_{43} = 1.78796740242292$$
$$x_{43} = 67.5444174374737$$
$$x_{43} = -31.4239545634883$$
$$x_{43} = -0.589149345698636$$
$$x_{43} = -59.6944752084758$$
$$x_{43} = -72.2601090360426$$
$$x_{43} = 26.7215715058841$$
$$x_{43} = -22.0027089238939$$
$$x_{43} = -12.5866832131152$$
$$x_{43} = 42.4117793291063$$
$$x_{43} = 7.91292734920106$$
$$x_{43} = 73.8275878854089$$
$$x_{43} = 45.5637266141872$$
$$x_{43} = 80.1107606545324$$
$$x_{43} = -43.9880174241053$$
$$x_{43} = -65.9772568416673$$
$$x_{43} = -28.2832927385975$$
$$x_{43} = 20.4438287899401$$
$$x_{43} = 89.5408213115049$$
$$x_{43} = -75.4015518300676$$
$$x_{43} = -9.45230877575799$$
$$x_{43} = 70.6927063810377$$
$$x_{43} = 23.5624430962496$$
$$x_{43} = 29.8455246822244$$
$$x_{43} = -50.2704838147943$$
$$x_{43} = 92.6771112747014$$
$$x_{43} = -81.6844802544329$$
$$x_{43} = -87.9674454907549$$
$$x_{43} = -53.4117892090852$$
$$x_{43} = -3.22844409727052$$
$$x_{43} = -6.32449323163835$$
$$x_{43} = 14.1707740307198$$
$$x_{43} = 36.128642014024$$
Decrece en los intervalos
$$\left[100.533444581925, \infty\right)$$
Crece en los intervalos
$$\left(-\infty, -102.101878220453\right]$$
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
$$\lim_{x \to -\infty}\left(\left(\left(- x 3 \cdot 7 \cos{\left(2 x \right)} + 2 \cos{\left(3 x \right)}\right) - 7 \cos{\left(2 x \right)}\right) - 14 \cos{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
$$y = \left\langle -\infty, \infty\right\rangle$$
$$\lim_{x \to \infty}\left(\left(\left(- x 3 \cdot 7 \cos{\left(2 x \right)} + 2 \cos{\left(3 x \right)}\right) - 7 \cos{\left(2 x \right)}\right) - 14 \cos{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = \left\langle -\infty, \infty\right\rangle$$
$$\lim_{x \to -\infty}\left(\left(\left(- x 3 \cdot 7 \cos{\left(2 x \right)} + 2 \cos{\left(3 x \right)}\right) - 7 \cos{\left(2 x \right)}\right) - 14 \cos{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
$$y = \left\langle -\infty, \infty\right\rangle$$
$$\lim_{x \to \infty}\left(\left(\left(- x 3 \cdot 7 \cos{\left(2 x \right)} + 2 \cos{\left(3 x \right)}\right) - 7 \cos{\left(2 x \right)}\right) - 14 \cos{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = \left\langle -\infty, \infty\right\rangle$$
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función 2*cos(3*x) - (7*cos(2*x))*3*x - 7*cos(2*x) - 14*cos(x), dividida por x con x->+oo y x ->-oo
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
$$y = x \lim_{x \to -\infty}\left(\frac{\left(\left(- x 3 \cdot 7 \cos{\left(2 x \right)} + 2 \cos{\left(3 x \right)}\right) - 7 \cos{\left(2 x \right)}\right) - 14 \cos{\left(x \right)}}{x}\right)$$
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
$$y = x \lim_{x \to \infty}\left(\frac{\left(\left(- x 3 \cdot 7 \cos{\left(2 x \right)} + 2 \cos{\left(3 x \right)}\right) - 7 \cos{\left(2 x \right)}\right) - 14 \cos{\left(x \right)}}{x}\right)$$
True
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
$$y = x \lim_{x \to -\infty}\left(\frac{\left(\left(- x 3 \cdot 7 \cos{\left(2 x \right)} + 2 \cos{\left(3 x \right)}\right) - 7 \cos{\left(2 x \right)}\right) - 14 \cos{\left(x \right)}}{x}\right)$$
True
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
$$y = x \lim_{x \to \infty}\left(\frac{\left(\left(- x 3 \cdot 7 \cos{\left(2 x \right)} + 2 \cos{\left(3 x \right)}\right) - 7 \cos{\left(2 x \right)}\right) - 14 \cos{\left(x \right)}}{x}\right)$$
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:
$$\left(\left(- x 3 \cdot 7 \cos{\left(2 x \right)} + 2 \cos{\left(3 x \right)}\right) - 7 \cos{\left(2 x \right)}\right) - 14 \cos{\left(x \right)} = 21 x \cos{\left(2 x \right)} - 14 \cos{\left(x \right)} - 7 \cos{\left(2 x \right)} + 2 \cos{\left(3 x \right)}$$
- No
$$\left(\left(- x 3 \cdot 7 \cos{\left(2 x \right)} + 2 \cos{\left(3 x \right)}\right) - 7 \cos{\left(2 x \right)}\right) - 14 \cos{\left(x \right)} = - 21 x \cos{\left(2 x \right)} + 14 \cos{\left(x \right)} + 7 \cos{\left(2 x \right)} - 2 \cos{\left(3 x \right)}$$
- No
es decir, función
no es
par ni impar
Pues, comprobamos:
$$\left(\left(- x 3 \cdot 7 \cos{\left(2 x \right)} + 2 \cos{\left(3 x \right)}\right) - 7 \cos{\left(2 x \right)}\right) - 14 \cos{\left(x \right)} = 21 x \cos{\left(2 x \right)} - 14 \cos{\left(x \right)} - 7 \cos{\left(2 x \right)} + 2 \cos{\left(3 x \right)}$$
- No
$$\left(\left(- x 3 \cdot 7 \cos{\left(2 x \right)} + 2 \cos{\left(3 x \right)}\right) - 7 \cos{\left(2 x \right)}\right) - 14 \cos{\left(x \right)} = - 21 x \cos{\left(2 x \right)} + 14 \cos{\left(x \right)} + 7 \cos{\left(2 x \right)} - 2 \cos{\left(3 x \right)}$$
- No
es decir, función
no es
par ni impar