Sr Examen

Gráfico de la función y = y=sin3x-3xcosx

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src]
f(x) = sin(3*x) - 3*x*cos(x)
f(x)=3xcos(x)+sin(3x)f{\left(x \right)} = - 3 x \cos{\left(x \right)} + \sin{\left(3 x \right)}
f = -3*x*cos(x) + sin(3*x)
Gráfico de la función
02468-8-6-4-2-1010-5050
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:
3xcos(x)+sin(3x)=0- 3 x \cos{\left(x \right)} + \sin{\left(3 x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=98.9635366664533x_{1} = -98.9635366664533
x2=89.5391131716313x_{2} = 89.5391131716313
x3=67.5491762080989x_{3} = -67.5491762080989
x4=48.7015291538919x_{4} = 48.7015291538919
x5=11.025687980839x_{5} = 11.025687980839
x6=39.2783919533992x_{6} = 39.2783919533992
x7=26.7160060657789x_{7} = -26.7160060657789
x8=23.5760713065118x_{8} = -23.5760713065118
x9=76.9733501642204x_{9} = -76.9733501642204
x10=45.5604080746893x_{10} = 45.5604080746893
x11=1.73927840278259x_{11} = 1.73927840278259
x12=51.8427073381864x_{12} = -51.8427073381864
x13=73.8319417184434x_{13} = -73.8319417184434
x14=23.5760713065118x_{14} = 23.5760713065118
x15=0x_{15} = 0
x16=92.6805796616328x_{16} = 92.6805796616328
x17=20.4366440624561x_{17} = 20.4366440624561
x18=29.8562887792909x_{18} = 29.8562887792909
x19=67.5491762080989x_{19} = 67.5491762080989
x20=11.025687980839x_{20} = -11.025687980839
x21=29.8562887792909x_{21} = -29.8562887792909
x22=26.7160060657789x_{22} = 26.7160060657789
x23=58.1251980218793x_{23} = 58.1251980218793
x24=7.89587700878652x_{24} = 7.89587700878652
x25=61.2664967587966x_{25} = 61.2664967587966
x26=95.8220544223783x_{26} = 95.8220544223783
x27=39.2783919533992x_{27} = -39.2783919533992
x28=86.3976558542627x_{28} = -86.3976558542627
x29=89.5391131716313x_{29} = -89.5391131716313
x30=42.4193567698246x_{30} = -42.4193567698246
x31=76.9733501642204x_{31} = 76.9733501642204
x32=265.46583487412x_{32} = -265.46583487412
x33=17.2979987451934x_{33} = -17.2979987451934
x34=7.89587700878652x_{34} = -7.89587700878652
x35=1.73927840278259x_{35} = -1.73927840278259
x36=83.2562087474756x_{36} = -83.2562087474756
x37=51.8427073381864x_{37} = 51.8427073381864
x38=36.1375361375219x_{38} = -36.1375361375219
x39=58.1251980218793x_{39} = -58.1251980218793
x40=86.3976558542627x_{40} = 86.3976558542627
x41=32.996820383096x_{41} = 32.996820383096
x42=73.8319417184434x_{42} = 73.8319417184434
x43=14.1606501178349x_{43} = 14.1606501178349
x44=4.78070746628939x_{44} = 4.78070746628939
x45=42.4193567698246x_{45} = 42.4193567698246
x46=70.6905496390197x_{46} = 70.6905496390197
x47=98.9635366664533x_{47} = 98.9635366664533
x48=17.2979987451934x_{48} = 17.2979987451934
x49=14.1606501178349x_{49} = -14.1606501178349
x50=48.7015291538919x_{50} = -48.7015291538919
x51=54.9839328497163x_{51} = 54.9839328497163
x52=92.6805796616328x_{52} = -92.6805796616328
x53=54.9839328497163x_{53} = -54.9839328497163
x54=45.5604080746893x_{54} = -45.5604080746893
x55=83.2562087474756x_{55} = 83.2562087474756
x56=61.2664967587966x_{56} = -61.2664967587966
x57=80.114773051938x_{57} = -80.114773051938
x58=80.114773051938x_{58} = 80.114773051938
x59=36.1375361375219x_{59} = 36.1375361375219
x60=4.78070746628939x_{60} = -4.78070746628939
x61=64.4078241527282x_{61} = 64.4078241527282
x62=70.6905496390197x_{62} = -70.6905496390197
x63=32.996820383096x_{63} = -32.996820383096
x64=20.4366440624561x_{64} = -20.4366440624561
x65=64.4078241527282x_{65} = -64.4078241527282
x66=95.8220544223783x_{66} = -95.8220544223783
Puntos de cruce con el eje de coordenadas Y
El gráfico cruce el eje Y cuando x es igual a 0:
sustituimos x = 0 en sin(3*x) - 3*x*cos(x).
sin(03)03cos(0)\sin{\left(0 \cdot 3 \right)} - 0 \cdot 3 \cos{\left(0 \right)}
Resultado:
f(0)=0f{\left(0 \right)} = 0
Punto:
(0, 0)
Extremos de la función
Para hallar los extremos hay que resolver la ecuación
ddxf(x)=0\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:
ddxf(x)=\frac{d}{d x} f{\left(x \right)} =
primera derivada
3xsin(x)3cos(x)+3cos(3x)=03 x \sin{\left(x \right)} - 3 \cos{\left(x \right)} + 3 \cos{\left(3 x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=65.9734457253857x_{1} = 65.9734457253857
x2=15.707963267949x_{2} = -15.707963267949
x3=8.57750497498977108x_{3} = -8.57750497498977 \cdot 10^{-8}
x4=37.6991118430775x_{4} = 37.6991118430775
x5=69.1150383789755x_{5} = -69.1150383789755
x6=34.5575191894877x_{6} = -34.5575191894877
x7=91.106186954104x_{7} = -91.106186954104
x8=0x_{8} = 0
x9=6.28318530717959x_{9} = 6.28318530717959
x10=47.1238898038469x_{10} = -47.1238898038469
x11=78.5398163397448x_{11} = -78.5398163397448
x12=28.2743338823081x_{12} = -28.2743338823081
x13=97.3893722612836x_{13} = 97.3893722612836
x14=3.14159265358979x_{14} = 3.14159265358979
x15=40.8407044966673x_{15} = 40.8407044966673
x16=62.8318530717959x_{16} = 62.8318530717959
x17=81.6814089933346x_{17} = -81.6814089933346
x18=43.9822971502571x_{18} = 43.9822971502571
x19=84.8230016469244x_{19} = -84.8230016469244
x20=100.530964914873x_{20} = 100.530964914873
x21=69.1150383789755x_{21} = 69.1150383789755
x22=94.2477796076938x_{22} = -94.2477796076938
x23=91.106186954104x_{23} = 91.106186954104
x24=78.5398163397448x_{24} = 78.5398163397448
x25=207.345115136926x_{25} = 207.345115136926
x26=47.1238898038469x_{26} = 47.1238898038469
x27=81.6814089933346x_{27} = 81.6814089933346
x28=72.2566310325652x_{28} = -72.2566310325652
x29=6.28318530717959x_{29} = -6.28318530717959
x30=28.2743338823081x_{30} = 28.2743338823081
x31=100.530964914873x_{31} = -100.530964914873
x32=65.9734457253857x_{32} = -65.9734457253857
x33=94.2477796076938x_{33} = 94.2477796076938
x34=31.4159265358979x_{34} = 31.4159265358979
x35=50.2654824574367x_{35} = 50.2654824574367
x36=21.9911485751286x_{36} = -21.9911485751286
x37=12.5663706143592x_{37} = 12.5663706143592
x38=1.23728839368491x_{38} = -1.23728839368491
x39=15.707963267949x_{39} = 15.707963267949
x40=75.398223686155x_{40} = -75.398223686155
x41=72.2566310325652x_{41} = 72.2566310325652
x42=18.8495559215388x_{42} = 18.8495559215388
x43=37.6991118430775x_{43} = -37.6991118430775
x44=50.2654824574367x_{44} = -50.2654824574367
x45=3.14159265358979x_{45} = -3.14159265358979
x46=87.9645943005142x_{46} = -87.9645943005142
x47=25.1327412287183x_{47} = -25.1327412287183
x48=40.8407044966673x_{48} = -40.8407044966673
x49=53.4070751110265x_{49} = 53.4070751110265
x50=9.42477796076938x_{50} = 9.42477796076938
x51=43.9822971502571x_{51} = -43.9822971502571
x52=56.5486677646163x_{52} = -56.5486677646163
x53=97.3893722612836x_{53} = -97.3893722612836
x54=59.6902604182061x_{54} = -59.6902604182061
x55=12.5663706143592x_{55} = -12.5663706143592
x56=18.8495559215388x_{56} = -18.8495559215388
x57=84.8230016469244x_{57} = 84.8230016469244
x58=25.1327412287183x_{58} = 25.1327412287183
x59=21.9911485751286x_{59} = 21.9911485751286
x60=59.6902604182061x_{60} = 59.6902604182061
x61=53.4070751110265x_{61} = -53.4070751110265
x62=31.4159265358979x_{62} = -31.4159265358979
x63=9.42477796076938x_{63} = -9.42477796076938
x64=62.8318530717959x_{64} = -62.8318530717959
x65=56.5486677646163x_{65} = 56.5486677646163
x66=75.398223686155x_{66} = 75.398223686155
x67=34.5575191894877x_{67} = 34.5575191894877
x68=87.9645943005142x_{68} = 87.9645943005142
Signos de extremos en los puntos:
(65.97344572538566, 197.920337176157)

(-15.707963267948966, -47.1238898038469)

(-8.577504974989769e-08, 1.90582413132218e-21)

(37.69911184307752, -113.097335529233)

(-69.11503837897546, 207.345115136926)

(-34.55751918948773, -103.672557568463)

(-91.106186954104, -273.318560862312)

(0, 0)

(6.283185307179586, -18.8495559215388)

(-47.1238898038469, -141.371669411541)

(-78.53981633974483, -235.619449019234)

(-28.274333882308138, -84.8230016469244)

(97.3893722612836, 292.168116783851)

(3.141592653589793, 9.42477796076938)

(40.840704496667314, 122.522113490002)

(62.83185307179586, -188.495559215388)

(-81.68140899333463, 245.044226980004)

(43.982297150257104, -131.946891450771)

(-84.82300164692441, -254.469004940773)

(100.53096491487338, -301.59289474462)

(69.11503837897546, -207.345115136926)

(-94.2477796076938, 282.743338823081)

(91.106186954104, 273.318560862312)

(78.53981633974483, 235.619449019234)

(207.34511513692635, -622.035345410779)

(47.1238898038469, 141.371669411541)

(81.68140899333463, -245.044226980004)

(-72.25663103256524, -216.769893097696)

(-6.283185307179586, 18.8495559215388)

(28.274333882308138, 84.8230016469244)

(-100.53096491487338, 301.59289474462)

(-65.97344572538566, -197.920337176157)

(94.2477796076938, -282.743338823081)

(31.41592653589793, -94.2477796076938)

(50.26548245743669, -150.79644737231)

(-21.991148575128552, -65.9734457253857)

(12.566370614359172, -37.6991118430775)

(-1.2372883936849146, 1.75497647171138)

(15.707963267948966, 47.1238898038469)

(-75.39822368615503, 226.194671058465)

(72.25663103256524, 216.769893097696)

(18.84955592153876, -56.5486677646163)

(-37.69911184307752, 113.097335529233)

(-50.26548245743669, 150.79644737231)

(-3.141592653589793, -9.42477796076938)

(-87.96459430051421, 263.893782901543)

(-25.132741228718345, 75.398223686155)

(-40.840704496667314, -122.522113490002)

(53.40707511102649, 160.221225333079)

(9.42477796076938, 28.2743338823081)

(-43.982297150257104, 131.946891450771)

(-56.548667764616276, 169.646003293849)

(-97.3893722612836, -292.168116783851)

(-59.69026041820607, -179.070781254618)

(-12.566370614359172, 37.6991118430775)

(-18.84955592153876, 56.5486677646163)

(84.82300164692441, 254.469004940773)

(25.132741228718345, -75.398223686155)

(21.991148575128552, 65.9734457253857)

(59.69026041820607, 179.070781254618)

(-53.40707511102649, -160.221225333079)

(-31.41592653589793, 94.2477796076938)

(-9.42477796076938, -28.2743338823081)

(-62.83185307179586, 188.495559215388)

(56.548667764616276, -169.646003293849)

(75.39822368615503, -226.194671058465)

(34.55751918948773, 103.672557568463)

(87.96459430051421, -263.893782901543)


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:
x1=15.707963267949x_{1} = -15.707963267949
x2=37.6991118430775x_{2} = 37.6991118430775
x3=34.5575191894877x_{3} = -34.5575191894877
x4=91.106186954104x_{4} = -91.106186954104
x5=6.28318530717959x_{5} = 6.28318530717959
x6=47.1238898038469x_{6} = -47.1238898038469
x7=78.5398163397448x_{7} = -78.5398163397448
x8=28.2743338823081x_{8} = -28.2743338823081
x9=62.8318530717959x_{9} = 62.8318530717959
x10=43.9822971502571x_{10} = 43.9822971502571
x11=84.8230016469244x_{11} = -84.8230016469244
x12=100.530964914873x_{12} = 100.530964914873
x13=69.1150383789755x_{13} = 69.1150383789755
x14=207.345115136926x_{14} = 207.345115136926
x15=81.6814089933346x_{15} = 81.6814089933346
x16=72.2566310325652x_{16} = -72.2566310325652
x17=65.9734457253857x_{17} = -65.9734457253857
x18=94.2477796076938x_{18} = 94.2477796076938
x19=31.4159265358979x_{19} = 31.4159265358979
x20=50.2654824574367x_{20} = 50.2654824574367
x21=21.9911485751286x_{21} = -21.9911485751286
x22=12.5663706143592x_{22} = 12.5663706143592
x23=18.8495559215388x_{23} = 18.8495559215388
x24=3.14159265358979x_{24} = -3.14159265358979
x25=40.8407044966673x_{25} = -40.8407044966673
x26=97.3893722612836x_{26} = -97.3893722612836
x27=59.6902604182061x_{27} = -59.6902604182061
x28=25.1327412287183x_{28} = 25.1327412287183
x29=53.4070751110265x_{29} = -53.4070751110265
x30=9.42477796076938x_{30} = -9.42477796076938
x31=56.5486677646163x_{31} = 56.5486677646163
x32=75.398223686155x_{32} = 75.398223686155
x33=87.9645943005142x_{33} = 87.9645943005142
Puntos máximos de la función:
x33=65.9734457253857x_{33} = 65.9734457253857
x33=69.1150383789755x_{33} = -69.1150383789755
x33=97.3893722612836x_{33} = 97.3893722612836
x33=3.14159265358979x_{33} = 3.14159265358979
x33=40.8407044966673x_{33} = 40.8407044966673
x33=81.6814089933346x_{33} = -81.6814089933346
x33=94.2477796076938x_{33} = -94.2477796076938
x33=91.106186954104x_{33} = 91.106186954104
x33=78.5398163397448x_{33} = 78.5398163397448
x33=47.1238898038469x_{33} = 47.1238898038469
x33=6.28318530717959x_{33} = -6.28318530717959
x33=28.2743338823081x_{33} = 28.2743338823081
x33=100.530964914873x_{33} = -100.530964914873
x33=1.23728839368491x_{33} = -1.23728839368491
x33=15.707963267949x_{33} = 15.707963267949
x33=75.398223686155x_{33} = -75.398223686155
x33=72.2566310325652x_{33} = 72.2566310325652
x33=37.6991118430775x_{33} = -37.6991118430775
x33=50.2654824574367x_{33} = -50.2654824574367
x33=87.9645943005142x_{33} = -87.9645943005142
x33=25.1327412287183x_{33} = -25.1327412287183
x33=53.4070751110265x_{33} = 53.4070751110265
x33=9.42477796076938x_{33} = 9.42477796076938
x33=43.9822971502571x_{33} = -43.9822971502571
x33=56.5486677646163x_{33} = -56.5486677646163
x33=12.5663706143592x_{33} = -12.5663706143592
x33=18.8495559215388x_{33} = -18.8495559215388
x33=84.8230016469244x_{33} = 84.8230016469244
x33=21.9911485751286x_{33} = 21.9911485751286
x33=59.6902604182061x_{33} = 59.6902604182061
x33=31.4159265358979x_{33} = -31.4159265358979
x33=62.8318530717959x_{33} = -62.8318530717959
x33=34.5575191894877x_{33} = 34.5575191894877
Decrece en los intervalos
[207.345115136926,)\left[207.345115136926, \infty\right)
Crece en los intervalos
(,97.3893722612836]\left(-\infty, -97.3893722612836\right]
Puntos de flexiones
Hallemos los puntos de flexiones, para eso hay que resolver la ecuación
d2dx2f(x)=0\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0
(la segunda derivada es igual a cero),
las raíces de la ecuación obtenida serán los puntos de flexión para el gráfico de la función indicado:
d2dx2f(x)=\frac{d^{2}}{d x^{2}} f{\left(x \right)} =
segunda derivada
3(xcos(x)+2sin(x)3sin(3x))=03 \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)} - 3 \sin{\left(3 x \right)}\right) = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=73.8942674580662x_{1} = 73.8942674580662
x2=83.3116425941505x_{2} = -83.3116425941505
x3=39.3917332394548x_{3} = -39.3917332394548
x4=70.7555640145184x_{4} = -70.7555640145184
x5=33.1293524947654x_{5} = -33.1293524947654
x6=23.7520821340798x_{6} = 23.7520821340798
x7=8.23728184762533x_{7} = -8.23728184762533
x8=55.066720110079x_{8} = -55.066720110079
x9=48.7943886446047x_{9} = 48.7943886446047
x10=36.2597618372194x_{10} = 36.2597618372194
x11=64.4789638089266x_{11} = 64.4789638089266
x12=0x_{12} = 0
x13=51.9302496447026x_{13} = -51.9302496447026
x14=33.1293524947654x_{14} = 33.1293524947654
x15=20.6333955304583x_{15} = 20.6333955304583
x16=23.7520821340798x_{16} = -23.7520821340798
x17=77.0331980973782x_{17} = -77.0331980973782
x18=58.2037095863508x_{18} = -58.2037095863508
x19=95.8703481983066x_{19} = -95.8703481983066
x20=0.804192752567497x_{20} = -0.804192752567497
x21=58.2037095863508x_{21} = 58.2037095863508
x22=42.5249715142372x_{22} = 42.5249715142372
x23=26.8749028684202x_{23} = -26.8749028684202
x24=42.5249715142372x_{24} = -42.5249715142372
x25=30.0008934865934x_{25} = 30.0008934865934
x26=80.1723304298506x_{26} = -80.1723304298506
x27=92.7304818624105x_{27} = 92.7304818624105
x28=11.3186939616225x_{28} = -11.3186939616225
x29=86.4511157489026x_{29} = 86.4511157489026
x30=80.1723304298506x_{30} = 80.1723304298506
x31=89.5907335732319x_{31} = 89.5907335732319
x32=92.7304818624105x_{32} = -92.7304818624105
x33=14.4143690880764x_{33} = 14.4143690880764
x34=95.8703481983066x_{34} = 95.8703481983066
x35=67.6171176893326x_{35} = -67.6171176893326
x36=30.0008934865934x_{36} = -30.0008934865934
x37=86.4511157489026x_{37} = -86.4511157489026
x38=48.7943886446047x_{38} = -48.7943886446047
x39=2.14990681531005x_{39} = 2.14990681531005
x40=45.6592491738769x_{40} = 45.6592491738769
x41=83.3116425941505x_{41} = 83.3116425941505
x42=45.6592491738769x_{42} = -45.6592491738769
x43=124.133012295988x_{43} = -124.133012295988
x44=51.9302496447026x_{44} = 51.9302496447026
x45=14.4143690880764x_{45} = -14.4143690880764
x46=2.14990681531005x_{46} = -2.14990681531005
x47=61.3411443570525x_{47} = -61.3411443570525
x48=99.0103216790996x_{48} = -99.0103216790996
x49=36.2597618372194x_{49} = -36.2597618372194
x50=17.5201886543806x_{50} = -17.5201886543806
x51=89.5907335732319x_{51} = -89.5907335732319
x52=67.6171176893326x_{52} = 67.6171176893326
x53=99.0103216790996x_{53} = 99.0103216790996
x54=61.3411443570525x_{54} = 61.3411443570525
x55=55.066720110079x_{55} = 55.066720110079
x56=20.6333955304583x_{56} = -20.6333955304583
x57=73.8942674580662x_{57} = -73.8942674580662
x58=64.4789638089266x_{58} = -64.4789638089266
x59=11.3186939616225x_{59} = 11.3186939616225
x60=39.3917332394548x_{60} = 39.3917332394548
x61=70.7555640145184x_{61} = 70.7555640145184
x62=26.8749028684202x_{62} = 26.8749028684202
x63=5.17675931536835x_{63} = -5.17675931536835
x64=0.804192752567497x_{64} = 0.804192752567497
x65=77.0331980973782x_{65} = 77.0331980973782
x66=17.5201886543806x_{66} = 17.5201886543806
x67=8.23728184762533x_{67} = 8.23728184762533

Intervalos de convexidad y concavidad:
Hallemos los intervales donde la función es convexa o cóncava, para eso veamos cómo se comporta la función en los puntos de flexiones:
Cóncava en los intervalos
[99.0103216790996,)\left[99.0103216790996, \infty\right)
Convexa en los intervalos
(,124.133012295988]\left(-\infty, -124.133012295988\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
limx(3xcos(x)+sin(3x))=,\lim_{x \to -\infty}\left(- 3 x \cos{\left(x \right)} + \sin{\left(3 x \right)}\right) = \left\langle -\infty, \infty\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=,y = \left\langle -\infty, \infty\right\rangle
limx(3xcos(x)+sin(3x))=,\lim_{x \to \infty}\left(- 3 x \cos{\left(x \right)} + \sin{\left(3 x \right)}\right) = \left\langle -\infty, \infty\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=,y = \left\langle -\infty, \infty\right\rangle
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función sin(3*x) - 3*x*cos(x), dividida por x con x->+oo y x ->-oo
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=xlimx(3xcos(x)+sin(3x)x)y = x \lim_{x \to -\infty}\left(\frac{- 3 x \cos{\left(x \right)} + \sin{\left(3 x \right)}}{x}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=xlimx(3xcos(x)+sin(3x)x)y = x \lim_{x \to \infty}\left(\frac{- 3 x \cos{\left(x \right)} + \sin{\left(3 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:
3xcos(x)+sin(3x)=3xcos(x)sin(3x)- 3 x \cos{\left(x \right)} + \sin{\left(3 x \right)} = 3 x \cos{\left(x \right)} - \sin{\left(3 x \right)}
- No
3xcos(x)+sin(3x)=3xcos(x)+sin(3x)- 3 x \cos{\left(x \right)} + \sin{\left(3 x \right)} = - 3 x \cos{\left(x \right)} + \sin{\left(3 x \right)}
- No
es decir, función
no es
par ni impar
Gráfico
Gráfico de la función y = y=sin3x-3xcosx