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

Gráfico de la función y = cos(x)*4*x

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
f(x) = cos(x)*4*x
f(x)=x4cos⁡(x)f{\left(x \right)} = x 4 \cos{\left(x \right)} 
f = x*(4*cos(x))
Gráfico de la función
02468-8-6-4-2-1010-100100
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:
x4cos⁡(x)=0x 4 \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=32.9867228626928x_{1} = 32.9867228626928
x2=73.8274273593601x_{2} = 73.8274273593601
x3=4.71238898038469x_{3} = 4.71238898038469
x4=39.2699081698724x_{4} = 39.2699081698724
x5=95.8185759344887x_{5} = 95.8185759344887
x6=45.553093477052x_{6} = 45.553093477052
x7=70.6858347057703x_{7} = 70.6858347057703
x8=−10.9955742875643x_{8} = -10.9955742875643
x9=−58.1194640914112x_{9} = -58.1194640914112
x10=−23.5619449019235x_{10} = -23.5619449019235
x11=26.7035375555132x_{11} = 26.7035375555132
x12=−26.7035375555132x_{12} = -26.7035375555132
x13=−89.5353906273091x_{13} = -89.5353906273091
x14=−17.2787595947439x_{14} = -17.2787595947439
x15=−42.4115008234622x_{15} = -42.4115008234622
x16=−61.261056745001x_{16} = -61.261056745001
x17=92.6769832808989x_{17} = 92.6769832808989
x18=−76.9690200129499x_{18} = -76.9690200129499
x19=−92.6769832808989x_{19} = -92.6769832808989
x20=−98.9601685880785x_{20} = -98.9601685880785
x21=61.261056745001x_{21} = 61.261056745001
x22=−54.9778714378214x_{22} = -54.9778714378214
x23=42.4115008234622x_{23} = 42.4115008234622
x24=−64.4026493985908x_{24} = -64.4026493985908
x25=67.5442420521806x_{25} = 67.5442420521806
x26=−7.85398163397448x_{26} = -7.85398163397448
x27=80.1106126665397x_{27} = 80.1106126665397
x28=−14.1371669411541x_{28} = -14.1371669411541
x29=14.1371669411541x_{29} = 14.1371669411541
x30=−1.5707963267949x_{30} = -1.5707963267949
x31=1.5707963267949x_{31} = 1.5707963267949
x32=29.845130209103x_{32} = 29.845130209103
x33=10.9955742875643x_{33} = 10.9955742875643
x34=17.2787595947439x_{34} = 17.2787595947439
x35=−51.8362787842316x_{35} = -51.8362787842316
x36=−29.845130209103x_{36} = -29.845130209103
x37=0x_{37} = 0
x38=−48.6946861306418x_{38} = -48.6946861306418
x39=−73.8274273593601x_{39} = -73.8274273593601
x40=23.5619449019235x_{40} = 23.5619449019235
x41=20.4203522483337x_{41} = 20.4203522483337
x42=−86.3937979737193x_{42} = -86.3937979737193
x43=54.9778714378214x_{43} = 54.9778714378214
x44=58.1194640914112x_{44} = 58.1194640914112
x45=51.8362787842316x_{45} = 51.8362787842316
x46=−67.5442420521806x_{46} = -67.5442420521806
x47=114.668131856027x_{47} = 114.668131856027
x48=−4.71238898038469x_{48} = -4.71238898038469
x49=−45.553093477052x_{49} = -45.553093477052
x50=−70.6858347057703x_{50} = -70.6858347057703
x51=48.6946861306418x_{51} = 48.6946861306418
x52=−83.2522053201295x_{52} = -83.2522053201295
x53=−114.668131856027x_{53} = -114.668131856027
x54=−95.8185759344887x_{54} = -95.8185759344887
x55=89.5353906273091x_{55} = 89.5353906273091
x56=−39.2699081698724x_{56} = -39.2699081698724
x57=76.9690200129499x_{57} = 76.9690200129499
x58=−32.9867228626928x_{58} = -32.9867228626928
x59=−20.4203522483337x_{59} = -20.4203522483337
x60=−36.1283155162826x_{60} = -36.1283155162826
x61=7.85398163397448x_{61} = 7.85398163397448
x62=−80.1106126665397x_{62} = -80.1106126665397
x63=86.3937979737193x_{63} = 86.3937979737193
x64=98.9601685880785x_{64} = 98.9601685880785
x65=36.1283155162826x_{65} = 36.1283155162826
x66=64.4026493985908x_{66} = 64.4026493985908
x67=83.2522053201295x_{67} = 83.2522053201295
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 (cos(x)*4)*x.
0⋅4cos⁡(0)0 \cdot 4 \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
−4xsin⁡(x)+4cos⁡(x)=0- 4 x \sin{\left(x \right)} + 4 \cos{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=6.43729817917195x_{1} = 6.43729817917195
x2=81.6936492356017x_{2} = 81.6936492356017
x3=9.52933440536196x_{3} = 9.52933440536196
x4=−12.6452872238566x_{4} = -12.6452872238566
x5=0.86033358901938x_{5} = 0.86033358901938
x6=15.7712848748159x_{6} = 15.7712848748159
x7=65.9885986984904x_{7} = 65.9885986984904
x8=62.8477631944545x_{8} = 62.8477631944545
x9=−97.3996388790738x_{9} = -97.3996388790738
x10=−65.9885986984904x_{10} = -65.9885986984904
x11=−25.1724463266467x_{11} = -25.1724463266467
x12=59.7070073053355x_{12} = 59.7070073053355
x13=75.4114834888481x_{13} = 75.4114834888481
x14=−53.4257904773947x_{14} = -53.4257904773947
x15=25.1724463266467x_{15} = 25.1724463266467
x16=50.2853663377737x_{16} = 50.2853663377737
x17=−40.8651703304881x_{17} = -40.8651703304881
x18=−28.309642854452x_{18} = -28.309642854452
x19=−72.270467060309x_{19} = -72.270467060309
x20=−78.5525459842429x_{20} = -78.5525459842429
x21=−87.9759605524932x_{21} = -87.9759605524932
x22=12.6452872238566x_{22} = 12.6452872238566
x23=3.42561845948173x_{23} = 3.42561845948173
x24=−6.43729817917195x_{24} = -6.43729817917195
x25=47.145097736761x_{25} = 47.145097736761
x26=56.5663442798215x_{26} = 56.5663442798215
x27=97.3996388790738x_{27} = 97.3996388790738
x28=−94.2583883450399x_{28} = -94.2583883450399
x29=−56.5663442798215x_{29} = -56.5663442798215
x30=−3.42561845948173x_{30} = -3.42561845948173
x31=100.540910786842x_{31} = 100.540910786842
x32=44.0050179208308x_{32} = 44.0050179208308
x33=−15.7712848748159x_{33} = -15.7712848748159
x34=72.270467060309x_{34} = 72.270467060309
x35=−34.5864242152889x_{35} = -34.5864242152889
x36=−22.0364967279386x_{36} = -22.0364967279386
x37=−91.1171613944647x_{37} = -91.1171613944647
x38=−31.4477146375462x_{38} = -31.4477146375462
x39=−59.7070073053355x_{39} = -59.7070073053355
x40=−9.52933440536196x_{40} = -9.52933440536196
x41=40.8651703304881x_{41} = 40.8651703304881
x42=34.5864242152889x_{42} = 34.5864242152889
x43=−37.7256128277765x_{43} = -37.7256128277765
x44=−50.2853663377737x_{44} = -50.2853663377737
x45=−47.145097736761x_{45} = -47.145097736761
x46=53.4257904773947x_{46} = 53.4257904773947
x47=−69.1295029738953x_{47} = -69.1295029738953
x48=−44.0050179208308x_{48} = -44.0050179208308
x49=−84.8347887180423x_{49} = -84.8347887180423
x50=22.0364967279386x_{50} = 22.0364967279386
x51=69.1295029738953x_{51} = 69.1295029738953
x52=−147.661626855354x_{52} = -147.661626855354
x53=−62.8477631944545x_{53} = -62.8477631944545
x54=78.5525459842429x_{54} = 78.5525459842429
x55=−116.247530303932x_{55} = -116.247530303932
x56=28.309642854452x_{56} = 28.309642854452
x57=31.4477146375462x_{57} = 31.4477146375462
x58=91.1171613944647x_{58} = 91.1171613944647
x59=−75.4114834888481x_{59} = -75.4114834888481
x60=18.90240995686x_{60} = 18.90240995686
x61=84.8347887180423x_{61} = 84.8347887180423
x62=37.7256128277765x_{62} = 37.7256128277765
x63=87.9759605524932x_{63} = 87.9759605524932
x64=94.2583883450399x_{64} = 94.2583883450399
x65=−81.6936492356017x_{65} = -81.6936492356017
x66=−100.540910786842x_{66} = -100.540910786842
x67=−18.90240995686x_{67} = -18.90240995686
x68=−0.86033358901938x_{68} = -0.86033358901938
Signos de extremos en los puntos:
(6.437298179171947, 25.4440157793354)

(81.69364923560168, 326.750117986098)

(9.529334405361963, -37.9091770379192)

(-12.645287223856643, -50.4237251915707)

(0.8603335890193797, 2.24438535276418)

(15.771284874815882, -62.9587078485349)

(65.98859869849039, -263.924091747167)

(62.84776319445445, 251.359235888618)

(-97.39963887907376, 389.578023182494)

(-65.98859869849039, 263.924091747167)

(-25.172446326646664, -100.610427271486)

(59.70700730533546, -238.794539361063)

(75.41148348884815, 301.619416292808)

(-53.42579047739466, 213.665736639585)

(25.172446326646664, 100.610427271486)

(50.28536633777365, 201.101704141589)

(-40.86517033048807, 163.41176185807)

(-28.30964285445201, 113.167990156377)

(-72.27046706030896, 289.054198392998)

(-78.55254598424293, 314.184726366937)

(-87.97596055249322, -351.881110929699)

(12.645287223856643, 50.4237251915707)

(3.4256184594817283, -13.1534855823636)

(-6.437298179171947, -25.4440157793354)

(47.14509773676103, -188.537983030168)

(56.56634427982152, 226.230028691505)

(97.39963887907376, -389.578023182494)

(-94.25838834503986, -377.012336900435)

(-56.56634427982152, -226.230028691505)

(-3.4256184594817283, 13.1534855823636)

(100.54091078684232, 402.143752223304)

(44.005017920830845, 175.974639916426)

(-15.771284874815882, 62.9587078485349)

(72.27046706030896, -289.054198392998)

(-34.58642421528892, 138.287906934354)

(-22.036496727938566, 88.0553683166339)

(-91.11716139446474, 364.446697798588)

(-31.447714637546234, -125.727309114138)

(-59.70700730533546, 238.794539361063)

(-9.529334405361963, 37.9091770379192)

(40.86517033048807, -163.41176185807)

(34.58642421528892, -138.287906934354)

(-37.7256128277765, -150.84946485124)

(-50.28536633777365, -201.101704141589)

(-47.14509773676103, 188.537983030168)

(53.42579047739466, -213.665736639585)

(-69.12950297389526, -276.489085227687)

(-44.005017920830845, -175.974639916426)

(-84.83478871804229, 339.315582094627)

(22.036496727938566, -88.0553683166339)

(69.12950297389526, 276.489085227687)

(-147.66162685535437, 590.632963406968)

(-62.84776319445445, -251.359235888618)

(78.55254598424293, -314.184726366937)

(-116.2475303039321, 464.972917503947)

(28.30964285445201, -113.167990156377)

(31.447714637546234, 125.727309114138)

(91.11716139446474, -364.446697798588)

(-75.41148348884815, -301.619416292808)

(18.902409956860023, 75.5040547918761)

(84.83478871804229, -339.315582094627)

(37.7256128277765, 150.84946485124)

(87.97596055249322, 351.881110929699)

(94.25838834503986, 377.012336900435)

(-81.69364923560168, -326.750117986098)

(-100.54091078684232, -402.143752223304)

(-18.902409956860023, -75.5040547918761)

(-0.8603335890193797, -2.24438535276418)


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=9.52933440536196x_{1} = 9.52933440536196
x2=−12.6452872238566x_{2} = -12.6452872238566
x3=15.7712848748159x_{3} = 15.7712848748159
x4=65.9885986984904x_{4} = 65.9885986984904
x5=−25.1724463266467x_{5} = -25.1724463266467
x6=59.7070073053355x_{6} = 59.7070073053355
x7=−87.9759605524932x_{7} = -87.9759605524932
x8=3.42561845948173x_{8} = 3.42561845948173
x9=−6.43729817917195x_{9} = -6.43729817917195
x10=47.145097736761x_{10} = 47.145097736761
x11=97.3996388790738x_{11} = 97.3996388790738
x12=−94.2583883450399x_{12} = -94.2583883450399
x13=−56.5663442798215x_{13} = -56.5663442798215
x14=72.270467060309x_{14} = 72.270467060309
x15=−31.4477146375462x_{15} = -31.4477146375462
x16=40.8651703304881x_{16} = 40.8651703304881
x17=34.5864242152889x_{17} = 34.5864242152889
x18=−37.7256128277765x_{18} = -37.7256128277765
x19=−50.2853663377737x_{19} = -50.2853663377737
x20=53.4257904773947x_{20} = 53.4257904773947
x21=−69.1295029738953x_{21} = -69.1295029738953
x22=−44.0050179208308x_{22} = -44.0050179208308
x23=22.0364967279386x_{23} = 22.0364967279386
x24=−62.8477631944545x_{24} = -62.8477631944545
x25=78.5525459842429x_{25} = 78.5525459842429
x26=28.309642854452x_{26} = 28.309642854452
x27=91.1171613944647x_{27} = 91.1171613944647
x28=−75.4114834888481x_{28} = -75.4114834888481
x29=84.8347887180423x_{29} = 84.8347887180423
x30=−81.6936492356017x_{30} = -81.6936492356017
x31=−100.540910786842x_{31} = -100.540910786842
x32=−18.90240995686x_{32} = -18.90240995686
x33=−0.86033358901938x_{33} = -0.86033358901938
Puntos máximos de la función:
x33=6.43729817917195x_{33} = 6.43729817917195
x33=81.6936492356017x_{33} = 81.6936492356017
x33=0.86033358901938x_{33} = 0.86033358901938
x33=62.8477631944545x_{33} = 62.8477631944545
x33=−97.3996388790738x_{33} = -97.3996388790738
x33=−65.9885986984904x_{33} = -65.9885986984904
x33=75.4114834888481x_{33} = 75.4114834888481
x33=−53.4257904773947x_{33} = -53.4257904773947
x33=25.1724463266467x_{33} = 25.1724463266467
x33=50.2853663377737x_{33} = 50.2853663377737
x33=−40.8651703304881x_{33} = -40.8651703304881
x33=−28.309642854452x_{33} = -28.309642854452
x33=−72.270467060309x_{33} = -72.270467060309
x33=−78.5525459842429x_{33} = -78.5525459842429
x33=12.6452872238566x_{33} = 12.6452872238566
x33=56.5663442798215x_{33} = 56.5663442798215
x33=−3.42561845948173x_{33} = -3.42561845948173
x33=100.540910786842x_{33} = 100.540910786842
x33=44.0050179208308x_{33} = 44.0050179208308
x33=−15.7712848748159x_{33} = -15.7712848748159
x33=−34.5864242152889x_{33} = -34.5864242152889
x33=−22.0364967279386x_{33} = -22.0364967279386
x33=−91.1171613944647x_{33} = -91.1171613944647
x33=−59.7070073053355x_{33} = -59.7070073053355
x33=−9.52933440536196x_{33} = -9.52933440536196
x33=−47.145097736761x_{33} = -47.145097736761
x33=−84.8347887180423x_{33} = -84.8347887180423
x33=69.1295029738953x_{33} = 69.1295029738953
x33=−147.661626855354x_{33} = -147.661626855354
x33=−116.247530303932x_{33} = -116.247530303932
x33=31.4477146375462x_{33} = 31.4477146375462
x33=18.90240995686x_{33} = 18.90240995686
x33=37.7256128277765x_{33} = 37.7256128277765
x33=87.9759605524932x_{33} = 87.9759605524932
x33=94.2583883450399x_{33} = 94.2583883450399
Decrece en los intervalos
[97.3996388790738,∞)\left[97.3996388790738, \infty\right)
Crece en los intervalos
(−∞,−100.540910786842]\left(-\infty, -100.540910786842\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
−4(xcos⁡(x)+2sin⁡(x))=0- 4 \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=39.3207281322521x_{1} = 39.3207281322521
x2=55.0142096788381x_{2} = 55.0142096788381
x3=73.8545010149048x_{3} = 73.8545010149048
x4=−33.0471686947054x_{4} = -33.0471686947054
x5=86.4169374541167x_{5} = 86.4169374541167
x6=29.9118938695518x_{6} = 29.9118938695518
x7=−20.5175229099417x_{7} = -20.5175229099417
x8=14.2763529183365x_{8} = 14.2763529183365
x9=−29.9118938695518x_{9} = -29.9118938695518
x10=−95.839441141233x_{10} = -95.839441141233
x11=11.17270586833x_{11} = 11.17270586833
x12=−76.9949898891676x_{12} = -76.9949898891676
x13=−51.8748140534268x_{13} = -51.8748140534268
x14=26.7780870755585x_{14} = 26.7780870755585
x15=−92.6985552433969x_{15} = -92.6985552433969
x16=−80.1355651940744x_{16} = -80.1355651940744
x17=−58.153842078645x_{17} = -58.153842078645
x18=−67.573830670859x_{18} = -67.573830670859
x19=45.5969279840735x_{19} = 45.5969279840735
x20=89.5577188827244x_{20} = 89.5577188827244
x21=−61.2936749662429x_{21} = -61.2936749662429
x22=−36.1835330907526x_{22} = -36.1835330907526
x23=8.09616360322292x_{23} = 8.09616360322292
x24=−55.0142096788381x_{24} = -55.0142096788381
x25=−14.2763529183365x_{25} = -14.2763529183365
x26=−42.458570771699x_{26} = -42.458570771699
x27=80.1355651940744x_{27} = 80.1355651940744
x28=95.839441141233x_{28} = 95.839441141233
x29=70.7141100665485x_{29} = 70.7141100665485
x30=−5.08698509410227x_{30} = -5.08698509410227
x31=−64.4336791037316x_{31} = -64.4336791037316
x32=0x_{32} = 0
x33=36.1835330907526x_{33} = 36.1835330907526
x34=−70.7141100665485x_{34} = -70.7141100665485
x35=61.2936749662429x_{35} = 61.2936749662429
x36=2.2889297281034x_{36} = 2.2889297281034
x37=23.6463238196036x_{37} = 23.6463238196036
x38=48.7357007949054x_{38} = 48.7357007949054
x39=−98.9803718651523x_{39} = -98.9803718651523
x40=−39.3207281322521x_{40} = -39.3207281322521
x41=−17.3932439645948x_{41} = -17.3932439645948
x42=83.2762171649775x_{42} = 83.2762171649775
x43=−86.4169374541167x_{43} = -86.4169374541167
x44=92.6985552433969x_{44} = 92.6985552433969
x45=51.8748140534268x_{45} = 51.8748140534268
x46=5.08698509410227x_{46} = 5.08698509410227
x47=−11.17270586833x_{47} = -11.17270586833
x48=−45.5969279840735x_{48} = -45.5969279840735
x49=33.0471686947054x_{49} = 33.0471686947054
x50=76.9949898891676x_{50} = 76.9949898891676
x51=−8.09616360322292x_{51} = -8.09616360322292
x52=64.4336791037316x_{52} = 64.4336791037316
x53=−48.7357007949054x_{53} = -48.7357007949054
x54=−26.7780870755585x_{54} = -26.7780870755585
x55=20.5175229099417x_{55} = 20.5175229099417
x56=17.3932439645948x_{56} = 17.3932439645948
x57=67.573830670859x_{57} = 67.573830670859
x58=58.153842078645x_{58} = 58.153842078645
x59=−23.6463238196036x_{59} = -23.6463238196036
x60=−73.8545010149048x_{60} = -73.8545010149048
x61=−2.2889297281034x_{61} = -2.2889297281034
x62=98.9803718651523x_{62} = 98.9803718651523
x63=−89.5577188827244x_{63} = -89.5577188827244
x64=−83.2762171649775x_{64} = -83.2762171649775
x65=42.458570771699x_{65} = 42.458570771699

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
[95.839441141233,∞)\left[95.839441141233, \infty\right)
Convexa en los intervalos
(−∞,−95.839441141233]\left(-\infty, -95.839441141233\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(x4cos⁡(x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(x 4 \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→∞(x4cos⁡(x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(x 4 \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 (cos(x)*4)*x, dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(4cos⁡(x))=⟨−4,4⟩\lim_{x \to -\infty}\left(4 \cos{\left(x \right)}\right) = \left\langle -4, 4\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=⟨−4,4⟩xy = \left\langle -4, 4\right\rangle x
lim⁡x→∞(4cos⁡(x))=⟨−4,4⟩\lim_{x \to \infty}\left(4 \cos{\left(x \right)}\right) = \left\langle -4, 4\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=⟨−4,4⟩xy = \left\langle -4, 4\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:
x4cos⁡(x)=−4xcos⁡(x)x 4 \cos{\left(x \right)} = - 4 x \cos{\left(x \right)}
- No
x4cos⁡(x)=4xcos⁡(x)x 4 \cos{\left(x \right)} = 4 x \cos{\left(x \right)}
- No
es decir, función
no es
par ni impar
Gráfico
Gráfico de la función y = cos(x)*4*x
    © Sr Examen – Калькулятор