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x^2*cos(2*x)
Trazado el gráfico de la función/ x^2*cos(2*x)

Gráfico de la función y = x^2*cos(2*x)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
        2         
f(x) = x *cos(2*x)
f(x)=x2cos⁡(2x)f{\left(x \right)} = x^{2} \cos{\left(2 x \right)} 
f = x^2*cos(2*x)
Gráfico de la función
02468-8-6-4-2-1010-200200
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:
x2cos⁡(2x)=0x^{2} \cos{\left(2 x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=0x_{1} = 0
x2=−3π4x_{2} = - \frac{3 \pi}{4}
x3=−π4x_{3} = - \frac{\pi}{4}
x4=π4x_{4} = \frac{\pi}{4}
x5=3π4x_{5} = \frac{3 \pi}{4}
Solución numérica
x1=−55.7632696012188x_{1} = -55.7632696012188
x2=−98.174770424681x_{2} = -98.174770424681
x3=66.7588438887831x_{3} = 66.7588438887831
x4=−11.7809724509617x_{4} = -11.7809724509617
x5=25.9181393921158x_{5} = 25.9181393921158
x6=−40.0553063332699x_{6} = -40.0553063332699
x7=18.0641577581413x_{7} = 18.0641577581413
x8=−13.3517687777566x_{8} = -13.3517687777566
x9=55.7632696012188x_{9} = 55.7632696012188
x10=−16.4933614313464x_{10} = -16.4933614313464
x11=−49.4800842940392x_{11} = -49.4800842940392
x12=96.6039740978861x_{12} = 96.6039740978861
x13=−41.6261026600648x_{13} = -41.6261026600648
x14=−22.776546738526x_{14} = -22.776546738526
x15=52.621676947629x_{15} = 52.621676947629
x16=76.1836218495525x_{16} = 76.1836218495525
x17=69.9004365423729x_{17} = 69.9004365423729
x18=30.6305283725005x_{18} = 30.6305283725005
x19=85.6083998103219x_{19} = 85.6083998103219
x20=−19.6349540849362x_{20} = -19.6349540849362
x21=−3.92699081698724x_{21} = -3.92699081698724
x22=38.484510006475x_{22} = 38.484510006475
x23=32.2013246992954x_{23} = 32.2013246992954
x24=27.4889357189107x_{24} = 27.4889357189107
x25=84.037603483527x_{25} = 84.037603483527
x26=−91.8915851175014x_{26} = -91.8915851175014
x27=98.174770424681x_{27} = 98.174770424681
x28=−85.6083998103219x_{28} = -85.6083998103219
x29=41.6261026600648x_{29} = 41.6261026600648
x30=91.8915851175014x_{30} = 91.8915851175014
x31=−2.35619449019234x_{31} = -2.35619449019234
x32=16.4933614313464x_{32} = 16.4933614313464
x33=46.3384916404494x_{33} = 46.3384916404494
x34=0x_{34} = 0
x35=71.4712328691678x_{35} = 71.4712328691678
x36=63.6172512351933x_{36} = 63.6172512351933
x37=54.1924732744239x_{37} = 54.1924732744239
x38=−84.037603483527x_{38} = -84.037603483527
x39=−93.4623814442964x_{39} = -93.4623814442964
x40=47.9092879672443x_{40} = 47.9092879672443
x41=24.3473430653209x_{41} = 24.3473430653209
x42=−5.49778714378214x_{42} = -5.49778714378214
x43=68.329640215578x_{43} = 68.329640215578
x44=62.0464549083984x_{44} = 62.0464549083984
x45=−68.329640215578x_{45} = -68.329640215578
x46=−38.484510006475x_{46} = -38.484510006475
x47=74.6128255227576x_{47} = 74.6128255227576
x48=−51.0508806208341x_{48} = -51.0508806208341
x49=5.49778714378214x_{49} = 5.49778714378214
x50=−0.785398163397448x_{50} = -0.785398163397448
x51=−47.9092879672443x_{51} = -47.9092879672443
x52=40.0553063332699x_{52} = 40.0553063332699
x53=−57.3340659280137x_{53} = -57.3340659280137
x54=49.4800842940392x_{54} = 49.4800842940392
x55=−25.9181393921158x_{55} = -25.9181393921158
x56=−76.1836218495525x_{56} = -76.1836218495525
x57=88.7499924639117x_{57} = 88.7499924639117
x58=99.7455667514759x_{58} = 99.7455667514759
x59=−62.0464549083984x_{59} = -62.0464549083984
x60=−82.4668071567321x_{60} = -82.4668071567321
x61=−71.4712328691678x_{61} = -71.4712328691678
x62=60.4756585816035x_{62} = 60.4756585816035
x63=−33.7721210260903x_{63} = -33.7721210260903
x64=77.7544181763474x_{64} = 77.7544181763474
x65=−46.3384916404494x_{65} = -46.3384916404494
x66=−63.6172512351933x_{66} = -63.6172512351933
x67=−90.3207887907066x_{67} = -90.3207887907066
x68=−35.3429173528852x_{68} = -35.3429173528852
x69=8.63937979737193x_{69} = 8.63937979737193
x70=−10.2101761241668x_{70} = -10.2101761241668
x71=−18.0641577581413x_{71} = -18.0641577581413
x72=−27.4889357189107x_{72} = -27.4889357189107
x73=−54.1924732744239x_{73} = -54.1924732744239
x74=3.92699081698724x_{74} = 3.92699081698724
x75=−79.3252145031423x_{75} = -79.3252145031423
x76=−99.7455667514759x_{76} = -99.7455667514759
x77=82.4668071567321x_{77} = 82.4668071567321
x78=33.7721210260903x_{78} = 33.7721210260903
x79=11.7809724509617x_{79} = 11.7809724509617
x80=10.2101761241668x_{80} = 10.2101761241668
x81=19.6349540849362x_{81} = 19.6349540849362
x82=−77.7544181763474x_{82} = -77.7544181763474
x83=−69.9004365423729x_{83} = -69.9004365423729
x84=2.35619449019234x_{84} = 2.35619449019234
x85=−24.3473430653209x_{85} = -24.3473430653209
x86=−60.4756585816035x_{86} = -60.4756585816035
x87=−80.8960108299372x_{87} = -80.8960108299372
x88=90.3207887907066x_{88} = 90.3207887907066
x89=−32.2013246992954x_{89} = -32.2013246992954
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 x^2*cos(2*x).
02cos⁡(0⋅2)0^{2} \cos{\left(0 \cdot 2 \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
−2x2sin⁡(2x)+2xcos⁡(2x)=0- 2 x^{2} \sin{\left(2 x \right)} + 2 x \cos{\left(2 x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−83.2582104451025x_{1} = -83.2582104451025
x2=−95.8237936557983x_{2} = -95.8237936557983
x3=−6.36114938588332x_{3} = -6.36114938588332
x4=−61.2692167254242x_{4} = -61.2692167254242
x5=42.4232846216546x_{5} = 42.4232846216546
x6=64.4104114951368x_{6} = 64.4104114951368
x7=−87.9702777935942x_{7} = -87.9702777935942
x8=−20.4447888830204x_{8} = -20.4447888830204
x9=51.8459215486945x_{9} = 51.8459215486945
x10=−97.3945058407034x_{10} = -97.3945058407034
x11=56.5575074028724x_{11} = 56.5575074028724
x12=−81.6875295729143x_{12} = -81.6875295729143
x13=−14.1723884348932x_{13} = -14.1723884348932
x14=20.4447888830204x_{14} = 20.4447888830204
x15=−59.6986350358615x_{15} = -59.6986350358615
x16=81.6875295729143x_{16} = 81.6875295729143
x17=34.5719777382463x_{17} = 34.5719777382463
x18=54.9869634999497x_{18} = 54.9869634999497
x19=−31.4318286143515x_{19} = -31.4318286143515
x20=67.5516432560125x_{20} = 67.5516432560125
x21=22.0138459496239x_{21} = 22.0138459496239
x22=−39.2826336922998x_{22} = -39.2826336922998
x23=−42.4232846216546x_{23} = -42.4232846216546
x24=43.9936604673443x_{24} = 43.9936604673443
x25=−7.91680570747386x_{25} = -7.91680570747386
x26=14.1723884348932x_{26} = 14.1723884348932
x27=0x_{27} = 0
x28=95.8237936557983x_{28} = 95.8237936557983
x29=−28.2919993689317x_{29} = -28.2919993689317
x30=92.682377840368x_{30} = 92.682377840368
x31=−29.8618677162152x_{31} = -29.8618677162152
x32=78.5461816776562x_{32} = 78.5461816776562
x33=15.739687460157x_{33} = 15.739687460157
x34=58.1280649399539x_{34} = 58.1280649399539
x35=23.5831338013883x_{35} = 23.5831338013883
x36=59.6986350358615x_{36} = 59.6986350358615
x37=−53.4164344328533x_{37} = -53.4164344328533
x38=28.2919993689317x_{38} = 28.2919993689317
x39=37.7123669872618x_{39} = 37.7123669872618
x40=−64.4104114951368x_{40} = -64.4104114951368
x41=73.8341988749761x_{41} = 73.8341988749761
x42=−50.275426362712x_{42} = -50.275426362712
x43=9.47734088326452x_{43} = 9.47734088326452
x44=80.1168532266283x_{44} = 80.1168532266283
x45=100.535938096812x_{45} = 100.535938096812
x46=−73.8341988749761x_{46} = -73.8341988749761
x47=−67.5516432560125x_{47} = -67.5516432560125
x48=−94.2530842748465x_{48} = -94.2530842748465
x49=26.7222398348818x_{49} = 26.7222398348818
x50=−43.9936604673443x_{50} = -43.9936604673443
x51=−1.8217985837127x_{51} = -1.8217985837127
x52=65.9810230816998x_{52} = 65.9810230816998
x53=−58.1280649399539x_{53} = -58.1280649399539
x54=87.9702777935942x_{54} = 87.9702777935942
x55=12.6059515321053x_{55} = 12.6059515321053
x56=−17.3076165276153x_{56} = -17.3076165276153
x57=94.2530842748465x_{57} = 94.2530842748465
x58=−51.8459215486945x_{58} = -51.8459215486945
x59=7.91680570747386x_{59} = 7.91680570747386
x60=−65.9810230816998x_{60} = -65.9810230816998
x61=−80.1168532266283x_{61} = -80.1168532266283
x62=1.8217985837127x_{62} = 1.8217985837127
x63=−23.5831338013883x_{63} = -23.5831338013883
x64=−89.5409744308928x_{64} = -89.5409744308928
x65=45.5640652755696x_{65} = 45.5640652755696
x66=−9.47734088326452x_{66} = -9.47734088326452
x67=−36.1421462518412x_{67} = -36.1421462518412
x68=89.5409744308928x_{68} = 89.5409744308928
x69=−15.739687460157x_{69} = -15.739687460157
x70=−22.0138459496239x_{70} = -22.0138459496239
x71=86.3995847801759x_{71} = 86.3995847801759
x72=−3.28916686636117x_{72} = -3.28916686636117
x73=6.36114938588332x_{73} = 6.36114938588332
x74=29.8618677162152x_{74} = 29.8618677162152
x75=−86.3995847801759x_{75} = -86.3995847801759
x76=50.275426362712x_{76} = 50.275426362712
x77=−75.4048541703099x_{77} = -75.4048541703099
x78=−37.7123669872618x_{78} = -37.7123669872618
x79=70.6929070794294x_{79} = 70.6929070794294
x80=−102.10665792544x_{80} = -102.10665792544
x81=72.2635497085721x_{81} = 72.2635497085721
x82=−45.5640652755696x_{82} = -45.5640652755696
x83=−72.2635497085721x_{83} = -72.2635497085721
x84=48.7049505853361x_{84} = 48.7049505853361
x85=36.1421462518412x_{85} = 36.1421462518412
Signos de extremos en los puntos:
(-83.25821044510252, -6931.42966061197)

(-95.8237936557983, -9181.69947142519)

(-6.3611493858833175, 39.9733021363577)

(-61.26921672542418, -3753.41701802048)

(42.423284621654574, -1799.23528635748)

(64.41041149513676, -4148.20119934443)

(-87.9702777935942, 7738.26982353423)

(-20.444788883020422, -417.490287838339)

(51.845921548694534, -2687.4997206991)

(-97.39450584070339, 9485.18980748457)

(56.55750740287244, 3198.25176082867)

(-81.68752957291433, 6672.35254391659)

(-14.172388434893186, -200.358453240761)

(20.444788883020422, -417.490287838339)

(-59.698635035861535, 3563.42713034141)

(81.68752957291433, 6672.35254391659)

(34.5719777382463, 1194.72195826454)

(54.9869634999497, -3023.06627893636)

(-31.431828614351502, 987.460229292167)

(67.55164325601251, -4562.72458875131)

(22.01384594962394, 484.110185984573)

(-39.28263369229977, -1542.62555268556)

(-42.423284621654574, -1799.23528635748)

(43.99366046734435, 1934.94235498677)

(-7.916805707473859, -62.1817173222964)

(14.172388434893186, -200.358453240761)

(0, 0)

(95.8237936557983, -9181.69947142519)

(-28.29199936893172, 799.937696298369)

(92.68237784036805, -8589.52320579581)

(-29.86186771621523, -891.231563638471)

(78.54618167765616, 6169.00271691402)

(15.739687460157024, 247.239269966989)

(58.128064939953894, -3378.37204461992)

(23.58313380138835, -555.664873146794)

(59.698635035861535, 3563.42713034141)

(-53.41643443285332, 2852.815598907)

(28.29199936893172, 799.937696298369)

(37.7123669872618, 1421.72288729931)

(-64.41041149513676, -4148.20119934443)

(73.83419887497614, -5450.98899228756)

(-50.27542636271201, 2527.11864426458)

(9.477340883264521, 89.3241268733139)

(80.11685322662832, -6418.21022935247)

(100.53593809681207, 10106.9748861042)

(-73.83419887497614, -5450.98899228756)

(-67.55164325601251, -4562.72458875131)

(-94.25308427484653, 8883.14393752977)

(26.722239834881776, -713.578626333476)

(-43.99366046734435, 1934.94235498677)

(-1.8217985837127004, -2.90945730293889)

(65.9810230816998, 4352.995493029)

(-58.128064939953894, -3378.37204461992)

(87.9702777935942, 7738.26982353423)

(12.60595153210529, 158.412361548588)

(-17.30761652761529, -299.054838257359)

(94.25308427484653, 8883.14393752977)

(-51.845921548694534, -2687.4997206991)

(7.916805707473859, -62.1817173222964)

(-65.9810230816998, 4352.995493029)

(-80.11685322662832, -6418.21022935247)

(1.8217985837127004, -2.90945730293889)

(-23.58313380138835, -555.664873146794)

(-89.54097443089285, -8017.08614880113)

(45.56406527556965, -2075.58422499242)

(-9.477340883264521, 89.3241268733139)

(-36.14214625184125, -1305.75502258676)

(89.54097443089285, -8017.08614880113)

(-15.739687460157024, 247.239269966989)

(-22.01384594962394, 484.110185984573)

(86.39958478017586, -7464.38830041637)

(-3.2891668663611693, 10.3508105527216)

(6.3611493858833175, 39.9733021363577)

(29.86186771621523, -891.231563638471)

(-86.39958478017586, -7464.38830041637)

(50.27542636271201, 2527.11864426458)

(-75.4048541703099, 5685.39209838875)

(-37.7123669872618, 1421.72288729931)

(70.69290707942938, -4996.98718636604)

(-102.10665792544042, -10425.2696286686)

(72.26354970857213, 5221.5206882831)

(-45.56406527556965, -2075.58422499242)

(-72.26354970857213, 5221.5206882831)

(48.70495058533613, -2371.67236954748)

(36.14214625184125, -1305.75502258676)


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=−83.2582104451025x_{1} = -83.2582104451025
x2=−95.8237936557983x_{2} = -95.8237936557983
x3=−61.2692167254242x_{3} = -61.2692167254242
x4=42.4232846216546x_{4} = 42.4232846216546
x5=64.4104114951368x_{5} = 64.4104114951368
x6=−20.4447888830204x_{6} = -20.4447888830204
x7=51.8459215486945x_{7} = 51.8459215486945
x8=−14.1723884348932x_{8} = -14.1723884348932
x9=20.4447888830204x_{9} = 20.4447888830204
x10=54.9869634999497x_{10} = 54.9869634999497
x11=67.5516432560125x_{11} = 67.5516432560125
x12=−39.2826336922998x_{12} = -39.2826336922998
x13=−42.4232846216546x_{13} = -42.4232846216546
x14=−7.91680570747386x_{14} = -7.91680570747386
x15=14.1723884348932x_{15} = 14.1723884348932
x16=0x_{16} = 0
x17=95.8237936557983x_{17} = 95.8237936557983
x18=92.682377840368x_{18} = 92.682377840368
x19=−29.8618677162152x_{19} = -29.8618677162152
x20=58.1280649399539x_{20} = 58.1280649399539
x21=23.5831338013883x_{21} = 23.5831338013883
x22=−64.4104114951368x_{22} = -64.4104114951368
x23=73.8341988749761x_{23} = 73.8341988749761
x24=80.1168532266283x_{24} = 80.1168532266283
x25=−73.8341988749761x_{25} = -73.8341988749761
x26=−67.5516432560125x_{26} = -67.5516432560125
x27=26.7222398348818x_{27} = 26.7222398348818
x28=−1.8217985837127x_{28} = -1.8217985837127
x29=−58.1280649399539x_{29} = -58.1280649399539
x30=−17.3076165276153x_{30} = -17.3076165276153
x31=−51.8459215486945x_{31} = -51.8459215486945
x32=7.91680570747386x_{32} = 7.91680570747386
x33=−80.1168532266283x_{33} = -80.1168532266283
x34=1.8217985837127x_{34} = 1.8217985837127
x35=−23.5831338013883x_{35} = -23.5831338013883
x36=−89.5409744308928x_{36} = -89.5409744308928
x37=45.5640652755696x_{37} = 45.5640652755696
x38=−36.1421462518412x_{38} = -36.1421462518412
x39=89.5409744308928x_{39} = 89.5409744308928
x40=86.3995847801759x_{40} = 86.3995847801759
x41=29.8618677162152x_{41} = 29.8618677162152
x42=−86.3995847801759x_{42} = -86.3995847801759
x43=70.6929070794294x_{43} = 70.6929070794294
x44=−102.10665792544x_{44} = -102.10665792544
x45=−45.5640652755696x_{45} = -45.5640652755696
x46=48.7049505853361x_{46} = 48.7049505853361
x47=36.1421462518412x_{47} = 36.1421462518412
Puntos máximos de la función:
x47=−6.36114938588332x_{47} = -6.36114938588332
x47=−87.9702777935942x_{47} = -87.9702777935942
x47=−97.3945058407034x_{47} = -97.3945058407034
x47=56.5575074028724x_{47} = 56.5575074028724
x47=−81.6875295729143x_{47} = -81.6875295729143
x47=−59.6986350358615x_{47} = -59.6986350358615
x47=81.6875295729143x_{47} = 81.6875295729143
x47=34.5719777382463x_{47} = 34.5719777382463
x47=−31.4318286143515x_{47} = -31.4318286143515
x47=22.0138459496239x_{47} = 22.0138459496239
x47=43.9936604673443x_{47} = 43.9936604673443
x47=−28.2919993689317x_{47} = -28.2919993689317
x47=78.5461816776562x_{47} = 78.5461816776562
x47=15.739687460157x_{47} = 15.739687460157
x47=59.6986350358615x_{47} = 59.6986350358615
x47=−53.4164344328533x_{47} = -53.4164344328533
x47=28.2919993689317x_{47} = 28.2919993689317
x47=37.7123669872618x_{47} = 37.7123669872618
x47=−50.275426362712x_{47} = -50.275426362712
x47=9.47734088326452x_{47} = 9.47734088326452
x47=100.535938096812x_{47} = 100.535938096812
x47=−94.2530842748465x_{47} = -94.2530842748465
x47=−43.9936604673443x_{47} = -43.9936604673443
x47=65.9810230816998x_{47} = 65.9810230816998
x47=87.9702777935942x_{47} = 87.9702777935942
x47=12.6059515321053x_{47} = 12.6059515321053
x47=94.2530842748465x_{47} = 94.2530842748465
x47=−65.9810230816998x_{47} = -65.9810230816998
x47=−9.47734088326452x_{47} = -9.47734088326452
x47=−15.739687460157x_{47} = -15.739687460157
x47=−22.0138459496239x_{47} = -22.0138459496239
x47=−3.28916686636117x_{47} = -3.28916686636117
x47=6.36114938588332x_{47} = 6.36114938588332
x47=50.275426362712x_{47} = 50.275426362712
x47=−75.4048541703099x_{47} = -75.4048541703099
x47=−37.7123669872618x_{47} = -37.7123669872618
x47=72.2635497085721x_{47} = 72.2635497085721
x47=−72.2635497085721x_{47} = -72.2635497085721
Decrece en los intervalos
[95.8237936557983,∞)\left[95.8237936557983, \infty\right)
Crece en los intervalos
(−∞,−102.10665792544]\left(-\infty, -102.10665792544\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
2(−2x2cos⁡(2x)−4xsin⁡(2x)+cos⁡(2x))=02 \left(- 2 x^{2} \cos{\left(2 x \right)} - 4 x \sin{\left(2 x \right)} + \cos{\left(2 x \right)}\right) = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−90.3318579518897x_{1} = -90.3318579518897
x2=−84.0494998311237x_{2} = -84.0494998311237
x3=−47.930144101695x_{3} = -47.930144101695
x4=−11.8647627812596x_{4} = -11.8647627812596
x5=−77.7672752842204x_{5} = -77.7672752842204
x6=24.3882890711501x_{6} = 24.3882890711501
x7=−118.603553624159x_{7} = -118.603553624159
x8=−35.3711701601923x_{8} = -35.3711701601923
x9=−27.5252261604062x_{9} = -27.5252261604062
x10=46.3600535780469x_{10} = 46.3600535780469
x11=82.4789299804946x_{11} = 82.4789299804946
x12=−71.485219494487x_{12} = -71.485219494487
x13=−54.2109145166807x_{13} = -54.2109145166807
x14=−46.3600535780469x_{14} = -46.3600535780469
x15=40.080243352799x_{15} = 40.080243352799
x16=−7.20521580987913x_{16} = -7.20521580987913
x17=30.6631119969344x_{17} = 30.6631119969344
x18=52.6406679577742x_{18} = 52.6406679577742
x19=−85.6200779864556x_{19} = -85.6200779864556
x20=−10.3064537512873x_{20} = -10.3064537512873
x21=−82.4789299804946x_{21} = -82.4789299804946
x22=85.6200779864556x_{22} = 85.6200779864556
x23=90.3318579518897x_{23} = 90.3318579518897
x24=41.6501006836697x_{24} = 41.6501006836697
x25=91.9024651450768x_{25} = 91.9024651450768
x26=27.5252261604062x_{26} = 27.5252261604062
x27=−25.9566176842759x_{27} = -25.9566176842759
x28=−43.2200260968693x_{28} = -43.2200260968693
x29=−32.2323246113358x_{29} = -32.2323246113358
x30=62.0625641968143x_{30} = 62.0625641968143
x31=84.0494998311237x_{31} = 84.0494998311237
x32=−24.3882890711501x_{32} = -24.3882890711501
x33=18.1192084567332x_{33} = 18.1192084567332
x34=−13.4259105675651x_{34} = -13.4259105675651
x35=99.7555904129902x_{35} = 99.7555904129902
x36=93.4730786916273x_{36} = 93.4730786916273
x37=−41.6501006836697x_{37} = -41.6501006836697
x38=−2.69286482701401x_{38} = -2.69286482701401
x39=74.6262236335308x_{39} = 74.6262236335308
x40=−21.2527167414791x_{40} = -21.2527167414791
x41=−49.5002793344963x_{41} = -49.5002793344963
x42=−69.914737240867x_{42} = -69.914737240867
x43=−55.7811919921513x_{43} = -55.7811919921513
x44=25.9566176842759x_{44} = 25.9566176842759
x45=77.7672752842204x_{45} = 77.7672752842204
x46=−62.0625641968143x_{46} = -62.0625641968143
x47=47.930144101695x_{47} = 47.930144101695
x48=0.299870710513912x_{48} = 0.299870710513912
x49=−60.4921858795299x_{49} = -60.4921858795299
x50=11.8647627812596x_{50} = 11.8647627812596
x51=−76.1967438868066x_{51} = -76.1967438868066
x52=−79.3378171645386x_{52} = -79.3378171645386
x53=−93.4730786916273x_{53} = -93.4730786916273
x54=69.914737240867x_{54} = 69.914737240867
x55=38.5104624020857x_{55} = 38.5104624020857
x56=−98.1849544042822x_{56} = -98.1849544042822
x57=54.2109145166807x_{57} = 54.2109145166807
x58=−4.15699235547246x_{58} = -4.15699235547246
x59=−5.66982003470015x_{59} = -5.66982003470015
x60=2.69286482701401x_{60} = 2.69286482701401
x61=−18.1192084567332x_{61} = -18.1192084567332
x62=−63.6329631278185x_{62} = -63.6329631278185
x63=88.7612574491069x_{63} = 88.7612574491069
x64=76.1967438868066x_{64} = 76.1967438868066
x65=63.6329631278185x_{65} = 63.6329631278185
x66=7.20521580987913x_{66} = 7.20521580987913
x67=5.66982003470015x_{67} = 5.66982003470015
x68=−57.3514978490025x_{68} = -57.3514978490025
x69=10.3064537512873x_{69} = 10.3064537512873
x70=49.5002793344963x_{70} = 49.5002793344963
x71=−91.9024651450768x_{71} = -91.9024651450768
x72=68.3442694107828x_{72} = 68.3442694107828
x73=60.4921858795299x_{73} = 60.4921858795299
x74=33.8016838062824x_{74} = 33.8016838062824
x75=98.1849544042822x_{75} = 98.1849544042822
x76=16.5535887364368x_{76} = 16.5535887364368
x77=−99.7555904129902x_{77} = -99.7555904129902
x78=55.7811919921513x_{78} = 55.7811919921513
x79=32.2323246113358x_{79} = 32.2323246113358
x80=−33.8016838062824x_{80} = -33.8016838062824
x81=4.15699235547246x_{81} = 4.15699235547246
x82=−1.34448374959035x_{82} = -1.34448374959035
x83=−68.3442694107828x_{83} = -68.3442694107828
x84=71.485219494487x_{84} = 71.485219494487
x85=−40.080243352799x_{85} = -40.080243352799
x86=96.6143236061486x_{86} = 96.6143236061486
x87=−19.6856437760583x_{87} = -19.6856437760583
x88=−38.5104624020857x_{88} = -38.5104624020857
x89=19.6856437760583x_{89} = 19.6856437760583
x90=−162.583570312367x_{90} = -162.583570312367

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
[98.1849544042822,∞)\left[98.1849544042822, \infty\right)
Convexa en los intervalos
(−∞,−162.583570312367]\left(-\infty, -162.583570312367\right]
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función x^2*cos(2*x), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(xcos⁡(2x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(x \cos{\left(2 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→∞(xcos⁡(2x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(x \cos{\left(2 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:
x2cos⁡(2x)=x2cos⁡(2x)x^{2} \cos{\left(2 x \right)} = x^{2} \cos{\left(2 x \right)}
- Sí
x2cos⁡(2x)=−x2cos⁡(2x)x^{2} \cos{\left(2 x \right)} = - x^{2} \cos{\left(2 x \right)}
- No
es decir, función
es
par
Gráfico
Gráfico de la función y = x^2*cos(2*x)
    © Sr Examen – Калькулятор