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Trazado el gráfico de la función/ (4*x^3)*cos(x)

Gráfico de la función y = (4*x^3)*cos(x)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
          3       
f(x) = 4*x *cos(x)
f(x)=4x3cos⁡(x)f{\left(x \right)} = 4 x^{3} \cos{\left(x \right)} 
f = (4*x^3)*cos(x)
Gráfico de la función
02468-8-6-4-2-1010-1000010000
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:
4x3cos⁡(x)=04 x^{3} \cos{\left(x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=0x_{1} = 0
x2=−π2x_{2} = - \frac{\pi}{2}
x3=π2x_{3} = \frac{\pi}{2}
Solución numérica
x1=42.4115008234622x_{1} = 42.4115008234622
x2=54.9778714378214x_{2} = 54.9778714378214
x3=−86.3937979737193x_{3} = -86.3937979737193
x4=−98.9601685880785x_{4} = -98.9601685880785
x5=29.845130209103x_{5} = 29.845130209103
x6=−42.4115008234622x_{6} = -42.4115008234622
x7=89.5353906273091x_{7} = 89.5353906273091
x8=−95.8185759344887x_{8} = -95.8185759344887
x9=−64.4026493985908x_{9} = -64.4026493985908
x10=0x_{10} = 0
x11=14.1371669411541x_{11} = 14.1371669411541
x12=−17.2787595947439x_{12} = -17.2787595947439
x13=48.6946861306418x_{13} = 48.6946861306418
x14=−48.6946861306418x_{14} = -48.6946861306418
x15=−67.5442420521806x_{15} = -67.5442420521806
x16=−32.9867228626928x_{16} = -32.9867228626928
x17=−80.1106126665397x_{17} = -80.1106126665397
x18=83.2522053201295x_{18} = 83.2522053201295
x19=1.5707963267949x_{19} = 1.5707963267949
x20=10.9955742875643x_{20} = 10.9955742875643
x21=−7.85398163397448x_{21} = -7.85398163397448
x22=−76.9690200129499x_{22} = -76.9690200129499
x23=98.9601685880785x_{23} = 98.9601685880785
x24=−4.71238898038469x_{24} = -4.71238898038469
x25=36.1283155162826x_{25} = 36.1283155162826
x26=20.4203522483337x_{26} = 20.4203522483337
x27=23.5619449019235x_{27} = 23.5619449019235
x28=51.8362787842316x_{28} = 51.8362787842316
x29=−45.553093477052x_{29} = -45.553093477052
x30=45.553093477052x_{30} = 45.553093477052
x31=−1.5707963267949x_{31} = -1.5707963267949
x32=−10.9955742875643x_{32} = -10.9955742875643
x33=26.7035375555132x_{33} = 26.7035375555132
x34=67.5442420521806x_{34} = 67.5442420521806
x35=92.6769832808989x_{35} = 92.6769832808989
x36=−58.1194640914112x_{36} = -58.1194640914112
x37=73.8274273593601x_{37} = 73.8274273593601
x38=−39.2699081698724x_{38} = -39.2699081698724
x39=95.8185759344887x_{39} = 95.8185759344887
x40=−23.5619449019235x_{40} = -23.5619449019235
x41=−70.6858347057703x_{41} = -70.6858347057703
x42=80.1106126665397x_{42} = 80.1106126665397
x43=58.1194640914112x_{43} = 58.1194640914112
x44=−14.1371669411541x_{44} = -14.1371669411541
x45=32.9867228626928x_{45} = 32.9867228626928
x46=−83.2522053201295x_{46} = -83.2522053201295
x47=7.85398163397448x_{47} = 7.85398163397448
x48=−89.5353906273091x_{48} = -89.5353906273091
x49=−29.845130209103x_{49} = -29.845130209103
x50=76.9690200129499x_{50} = 76.9690200129499
x51=86.3937979737193x_{51} = 86.3937979737193
x52=70.6858347057703x_{52} = 70.6858347057703
x53=−26.7035375555132x_{53} = -26.7035375555132
x54=−36.1283155162826x_{54} = -36.1283155162826
x55=−92.6769832808989x_{55} = -92.6769832808989
x56=−51.8362787842316x_{56} = -51.8362787842316
x57=−73.8274273593601x_{57} = -73.8274273593601
x58=17.2787595947439x_{58} = 17.2787595947439
x59=64.4026493985908x_{59} = 64.4026493985908
x60=−20.4203522483337x_{60} = -20.4203522483337
x61=4.71238898038469x_{61} = 4.71238898038469
x62=−54.9778714378214x_{62} = -54.9778714378214
x63=39.2699081698724x_{63} = 39.2699081698724
x64=−61.261056745001x_{64} = -61.261056745001
x65=61.261056745001x_{65} = 61.261056745001
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 (4*x^3)*cos(x).
4⋅03cos⁡(0)4 \cdot 0^{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
−4x3sin⁡(x)+12x2cos⁡(x)=0- 4 x^{3} \sin{\left(x \right)} + 12 x^{2} \cos{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−9.72402747617551x_{1} = -9.72402747617551
x2=−72.2981021067071x_{2} = -72.2981021067071
x3=−87.9986725257711x_{3} = -87.9986725257711
x4=−84.8583399660622x_{4} = -84.8583399660622
x5=84.8583399660622x_{5} = 84.8583399660622
x6=81.7181040853573x_{6} = 81.7181040853573
x7=56.6016202331048x_{7} = 56.6016202331048
x8=40.913898225293x_{8} = 40.913898225293
x9=3.80876221919969x_{9} = 3.80876221919969
x10=0x_{10} = 0
x11=−75.4379705139506x_{11} = -75.4379705139506
x12=−97.4201569811411x_{12} = -97.4201569811411
x13=97.4201569811411x_{13} = 97.4201569811411
x14=22.12591435735x_{14} = 22.12591435735
x15=100.560788770886x_{15} = 100.560788770886
x16=−15.8945130636842x_{16} = -15.8945130636842
x17=−66.0188560490172x_{17} = -66.0188560490172
x18=66.0188560490172x_{18} = 66.0188560490172
x19=−22.12591435735x_{19} = -22.12591435735
x20=69.1583898858035x_{20} = 69.1583898858035
x21=−28.3796522911214x_{21} = -28.3796522911214
x22=−34.6438990396267x_{22} = -34.6438990396267
x23=−78.5779764426249x_{23} = -78.5779764426249
x24=37.7783560989567x_{24} = 37.7783560989567
x25=−25.2509941253717x_{25} = -25.2509941253717
x26=−59.7404355133729x_{26} = -59.7404355133729
x27=12.7966483902814x_{27} = 12.7966483902814
x28=−62.8795272030449x_{28} = -62.8795272030449
x29=−6.70395577578075x_{29} = -6.70395577578075
x30=−1.19245882933643x_{30} = -1.19245882933643
x31=91.1390917936668x_{31} = 91.1390917936668
x32=47.1873806732917x_{32} = 47.1873806732917
x33=44.0502961191214x_{33} = 44.0502961191214
x34=1.19245882933643x_{34} = 1.19245882933643
x35=−56.6016202331048x_{35} = -56.6016202331048
x36=15.8945130636842x_{36} = 15.8945130636842
x37=−53.4631297645908x_{37} = -53.4631297645908
x38=62.8795272030449x_{38} = 62.8795272030449
x39=−40.913898225293x_{39} = -40.913898225293
x40=19.0061082873963x_{40} = 19.0061082873963
x41=6.70395577578075x_{41} = 6.70395577578075
x42=78.5779764426249x_{42} = 78.5779764426249
x43=72.2981021067071x_{43} = 72.2981021067071
x44=−31.510845756676x_{44} = -31.510845756676
x45=31.510845756676x_{45} = 31.510845756676
x46=−44.0502961191214x_{46} = -44.0502961191214
x47=−50.325024483292x_{47} = -50.325024483292
x48=75.4379705139506x_{48} = 75.4379705139506
x49=50.325024483292x_{49} = 50.325024483292
x50=59.7404355133729x_{50} = 59.7404355133729
x51=−94.2795891235637x_{51} = -94.2795891235637
x52=−19.0061082873963x_{52} = -19.0061082873963
x53=−100.560788770886x_{53} = -100.560788770886
x54=−37.7783560989567x_{54} = -37.7783560989567
x55=−3.80876221919969x_{55} = -3.80876221919969
x56=87.9986725257711x_{56} = 87.9986725257711
x57=9.72402747617551x_{57} = 9.72402747617551
x58=53.4631297645908x_{58} = 53.4631297645908
x59=−12.7966483902814x_{59} = -12.7966483902814
x60=−81.7181040853573x_{60} = -81.7181040853573
x61=25.2509941253717x_{61} = 25.2509941253717
x62=28.3796522911214x_{62} = 28.3796522911214
x63=34.6438990396267x_{63} = 34.6438990396267
x64=−91.1390917936668x_{64} = -91.1390917936668
x65=94.2795891235637x_{65} = 94.2795891235637
x66=−69.1583898858035x_{66} = -69.1583898858035
x67=−47.1873806732917x_{67} = -47.1873806732917
Signos de extremos en los puntos:
(-9.72402747617551, 3514.43550360095)

(-72.29810210670713, 1510313.53335791)

(-87.99867252577111, -2724182.04559702)

(-84.85833996606219, 2442712.51279198)

(84.85833996606219, -2442712.51279198)

(81.71810408535728, 2181335.04597451)

(56.60162023310481, 724331.58435522)

(40.91389822529297, -273217.30613698)

(3.808762219199689, -173.620051816331)

(0, 0)

(-75.43797051395065, -1715879.70709431)

(-97.42015698114113, 3696584.54759441)

(97.42015698114113, -3696584.54759441)

(22.125914357349984, -42934.6461855845)

(100.56078877088648, 4065863.85192867)

(-15.894513063684203, 15783.3987495175)

(-66.01885604901719, 1149783.42283034)

(66.01885604901719, -1149783.42283034)

(-22.125914357349984, 42934.6461855845)

(69.15838988580347, 1321862.8222492)

(-28.37965229112142, 90921.8253044151)

(-34.64389903962671, 165698.289727675)

(-78.57797644262494, 1939305.49434903)

(37.77835609895673, 214992.901302738)

(-25.25099412537165, -63951.6564937612)

(-59.74043551337287, 851761.955001316)

(12.796648390281426, 8160.76026338815)

(-62.87952720304487, -993331.184104639)

(-6.703955775780748, -1100.06136834542)

(-1.1924588293364287, -2.50529519287726)

(91.13909179366682, -3026487.7951639)

(47.18738067329166, -419432.109446505)

(44.05029611912139, 341115.657892607)

(1.1924588293364287, 2.50529519287726)

(-56.60162023310481, -724331.58435522)

(15.894513063684203, -15783.3987495175)

(-53.463129764590846, 610295.920879583)

(62.87952720304487, 993331.184104639)

(-40.91389822529297, 273217.30613698)

(19.006108287396344, 27126.6224448194)

(6.703955775780748, 1100.06136834542)

(78.57797644262494, -1939305.49434903)

(72.29810210670713, -1510313.53335791)

(-31.51084575667604, -124589.316590486)

(31.51084575667604, 124589.316590486)

(-44.05029611912139, -341115.657892607)

(-50.32502448329199, -508910.813128767)

(75.43797051395065, 1715879.70709431)

(50.32502448329199, 508910.813128767)

(59.74043551337287, -851761.955001316)

(-94.27958912356374, -3350373.91224916)

(-19.006108287396344, -27126.6224448194)

(-100.56078877088648, -4065863.85192867)

(-37.77835609895673, -214992.901302738)

(-3.808762219199689, 173.620051816331)

(87.99867252577111, 2724182.04559702)

(9.72402747617551, -3514.43550360095)

(53.463129764590846, -610295.920879583)

(-12.796648390281426, -8160.76026338815)

(-81.71810408535728, -2181335.04597451)

(25.25099412537165, 63951.6564937612)

(28.37965229112142, -90921.8253044151)

(34.64389903962671, -165698.289727675)

(-91.13909179366682, 3026487.7951639)

(94.27958912356374, 3350373.91224916)

(-69.15838988580347, -1321862.8222492)

(-47.18738067329166, 419432.109446505)


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=−87.9986725257711x_{1} = -87.9986725257711
x2=84.8583399660622x_{2} = 84.8583399660622
x3=40.913898225293x_{3} = 40.913898225293
x4=3.80876221919969x_{4} = 3.80876221919969
x5=−75.4379705139506x_{5} = -75.4379705139506
x6=97.4201569811411x_{6} = 97.4201569811411
x7=22.12591435735x_{7} = 22.12591435735
x8=66.0188560490172x_{8} = 66.0188560490172
x9=−25.2509941253717x_{9} = -25.2509941253717
x10=−62.8795272030449x_{10} = -62.8795272030449
x11=−6.70395577578075x_{11} = -6.70395577578075
x12=−1.19245882933643x_{12} = -1.19245882933643
x13=91.1390917936668x_{13} = 91.1390917936668
x14=47.1873806732917x_{14} = 47.1873806732917
x15=−56.6016202331048x_{15} = -56.6016202331048
x16=15.8945130636842x_{16} = 15.8945130636842
x17=78.5779764426249x_{17} = 78.5779764426249
x18=72.2981021067071x_{18} = 72.2981021067071
x19=−31.510845756676x_{19} = -31.510845756676
x20=−44.0502961191214x_{20} = -44.0502961191214
x21=−50.325024483292x_{21} = -50.325024483292
x22=59.7404355133729x_{22} = 59.7404355133729
x23=−94.2795891235637x_{23} = -94.2795891235637
x24=−19.0061082873963x_{24} = -19.0061082873963
x25=−100.560788770886x_{25} = -100.560788770886
x26=−37.7783560989567x_{26} = -37.7783560989567
x27=9.72402747617551x_{27} = 9.72402747617551
x28=53.4631297645908x_{28} = 53.4631297645908
x29=−12.7966483902814x_{29} = -12.7966483902814
x30=−81.7181040853573x_{30} = -81.7181040853573
x31=28.3796522911214x_{31} = 28.3796522911214
x32=34.6438990396267x_{32} = 34.6438990396267
x33=−69.1583898858035x_{33} = -69.1583898858035
Puntos máximos de la función:
x33=−9.72402747617551x_{33} = -9.72402747617551
x33=−72.2981021067071x_{33} = -72.2981021067071
x33=−84.8583399660622x_{33} = -84.8583399660622
x33=81.7181040853573x_{33} = 81.7181040853573
x33=56.6016202331048x_{33} = 56.6016202331048
x33=−97.4201569811411x_{33} = -97.4201569811411
x33=100.560788770886x_{33} = 100.560788770886
x33=−15.8945130636842x_{33} = -15.8945130636842
x33=−66.0188560490172x_{33} = -66.0188560490172
x33=−22.12591435735x_{33} = -22.12591435735
x33=69.1583898858035x_{33} = 69.1583898858035
x33=−28.3796522911214x_{33} = -28.3796522911214
x33=−34.6438990396267x_{33} = -34.6438990396267
x33=−78.5779764426249x_{33} = -78.5779764426249
x33=37.7783560989567x_{33} = 37.7783560989567
x33=−59.7404355133729x_{33} = -59.7404355133729
x33=12.7966483902814x_{33} = 12.7966483902814
x33=44.0502961191214x_{33} = 44.0502961191214
x33=1.19245882933643x_{33} = 1.19245882933643
x33=−53.4631297645908x_{33} = -53.4631297645908
x33=62.8795272030449x_{33} = 62.8795272030449
x33=−40.913898225293x_{33} = -40.913898225293
x33=19.0061082873963x_{33} = 19.0061082873963
x33=6.70395577578075x_{33} = 6.70395577578075
x33=31.510845756676x_{33} = 31.510845756676
x33=75.4379705139506x_{33} = 75.4379705139506
x33=50.325024483292x_{33} = 50.325024483292
x33=−3.80876221919969x_{33} = -3.80876221919969
x33=87.9986725257711x_{33} = 87.9986725257711
x33=25.2509941253717x_{33} = 25.2509941253717
x33=−91.1390917936668x_{33} = -91.1390917936668
x33=94.2795891235637x_{33} = 94.2795891235637
x33=−47.1873806732917x_{33} = -47.1873806732917
Decrece en los intervalos
[97.4201569811411,∞)\left[97.4201569811411, \infty\right)
Crece en los intervalos
(−∞,−100.560788770886]\left(-\infty, -100.560788770886\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
4x(−x2cos⁡(x)−6xsin⁡(x)+6cos⁡(x))=04 x \left(- x^{2} \cos{\left(x \right)} - 6 x \sin{\left(x \right)} + 6 \cos{\left(x \right)}\right) = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−36.2928915290304x_{1} = -36.2928915290304
x2=2.98146897551057x_{2} = 2.98146897551057
x3=14.538821316956x_{3} = 14.538821316956
x4=0x_{4} = 0
x5=42.5520407715344x_{5} = 42.5520407715344
x6=−70.7705144780994x_{6} = -70.7705144780994
x7=−23.811319714972x_{7} = -23.811319714972
x8=20.7061859967519x_{8} = 20.7061859967519
x9=−30.0435319479484x_{9} = -30.0435319479484
x10=39.4215265901233x_{10} = 39.4215265901233
x11=−14.538821316956x_{11} = -14.538821316956
x12=36.2928915290304x_{12} = 36.2928915290304
x13=−83.3241511438861x_{13} = -83.3241511438861
x14=95.8811126479692x_{14} = 95.8811126479692
x15=−64.495545315785x_{15} = -64.495545315785
x16=67.6328403186065x_{16} = 67.6328403186065
x17=99.0207249350603x_{17} = 99.0207249350603
x18=−95.8811126479692x_{18} = -95.8811126479692
x19=102.160458658341x_{19} = 102.160458658341
x20=−77.0468162058446x_{20} = -77.0468162058446
x21=89.6023032306285x_{21} = 89.6023032306285
x22=70.7705144780994x_{22} = 70.7705144780994
x23=73.9085198432299x_{23} = 73.9085198432299
x24=−42.5520407715344x_{24} = -42.5520407715344
x25=−80.185369601293x_{25} = -80.185369601293
x26=−11.495916748171x_{26} = -11.495916748171
x27=−20.7061859967519x_{27} = -20.7061859967519
x28=48.8172856736618x_{28} = 48.8172856736618
x29=5.63254352434708x_{29} = 5.63254352434708
x30=51.9515155836453x_{30} = 51.9515155836453
x31=58.2223356290493x_{31} = 58.2223356290493
x32=30.0435319479484x_{32} = 30.0435319479484
x33=−8.50941039706366x_{33} = -8.50941039706366
x34=86.4631361132255x_{34} = 86.4631361132255
x35=92.741634081119x_{35} = 92.741634081119
x36=−89.6023032306285x_{36} = -89.6023032306285
x37=−26.924570790473x_{37} = -26.924570790473
x38=−86.4631361132255x_{38} = -86.4631361132255
x39=11.495916748171x_{39} = 11.495916748171
x40=64.495545315785x_{40} = 64.495545315785
x41=8.50941039706366x_{41} = 8.50941039706366
x42=17.6130932998928x_{42} = 17.6130932998928
x43=−39.4215265901233x_{43} = -39.4215265901233
x44=−0.822926400561141x_{44} = -0.822926400561141
x45=−51.9515155836453x_{45} = -51.9515155836453
x46=−2.98146897551057x_{46} = -2.98146897551057
x47=−61.3586871153543x_{47} = -61.3586871153543
x48=83.3241511438861x_{48} = 83.3241511438861
x49=−55.0865764667238x_{49} = -55.0865764667238
x50=55.0865764667238x_{50} = 55.0865764667238
x51=−48.8172856736618x_{51} = -48.8172856736618
x52=−73.9085198432299x_{52} = -73.9085198432299
x53=26.924570790473x_{53} = 26.924570790473
x54=−5.63254352434708x_{54} = -5.63254352434708
x55=−33.1666524059798x_{55} = -33.1666524059798
x56=−99.0207249350603x_{56} = -99.0207249350603
x57=33.1666524059798x_{57} = 33.1666524059798
x58=−67.6328403186065x_{58} = -67.6328403186065
x59=−58.2223356290493x_{59} = -58.2223356290493
x60=61.3586871153543x_{60} = 61.3586871153543
x61=45.6840551197015x_{61} = 45.6840551197015
x62=77.0468162058446x_{62} = 77.0468162058446
x63=−92.741634081119x_{63} = -92.741634081119
x64=−17.6130932998928x_{64} = -17.6130932998928
x65=80.185369601293x_{65} = 80.185369601293
x66=−45.6840551197015x_{66} = -45.6840551197015
x67=23.811319714972x_{67} = 23.811319714972

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
[102.160458658341,∞)\left[102.160458658341, \infty\right)
Convexa en los intervalos
(−∞,−95.8811126479692]\left(-\infty, -95.8811126479692\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(4x3cos⁡(x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(4 x^{3} \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=⟨−∞,∞⟩y = \left\langle -\infty, \infty\right\rangle
lim⁡x→∞(4x3cos⁡(x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(4 x^{3} \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=⟨−∞,∞⟩y = \left\langle -\infty, \infty\right\rangle
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función (4*x^3)*cos(x), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(4x2cos⁡(x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(4 x^{2} \cos{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=⟨−∞,∞⟩xy = \left\langle -\infty, \infty\right\rangle x
lim⁡x→∞(4x2cos⁡(x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(4 x^{2} \cos{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=⟨−∞,∞⟩xy = \left\langle -\infty, \infty\right\rangle x
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:
4x3cos⁡(x)=−4x3cos⁡(x)4 x^{3} \cos{\left(x \right)} = - 4 x^{3} \cos{\left(x \right)}
- No
4x3cos⁡(x)=4x3cos⁡(x)4 x^{3} \cos{\left(x \right)} = 4 x^{3} \cos{\left(x \right)}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор