Sr Examen

Otras calculadoras


5*x^4*sin(3*x)+8

Gráfico de la función y = 5*x^4*sin(3*x)+8

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src]
          4             
f(x) = 5*x *sin(3*x) + 8
f(x)=5x4sin(3x)+8f{\left(x \right)} = 5 x^{4} \sin{\left(3 x \right)} + 8
f = (5*x^4)*sin(3*x) + 8
Gráfico de la función
02468-8-6-4-2-1010-100000100000
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:
5x4sin(3x)+8=05 x^{4} \sin{\left(3 x \right)} + 8 = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=95.2949771524232x_{1} = -95.2949771524232
x2=99.4837673582319x_{2} = -99.4837673582319
x3=4.19051973882574x_{3} = -4.19051973882574
x4=37.6991121071203x_{4} = -37.6991121071203
x5=65.9734457535385x_{5} = 65.9734457535385
x6=17.8023530604086x_{6} = -17.8023530604086
x7=41.8879018746255x_{7} = 41.8879018746255
x8=28.2743330478025x_{8} = -28.2743330478025
x9=59.690260376193x_{9} = -59.690260376193
x10=72.2566310521306x_{10} = 72.2566310521306
x11=27.227137301601x_{11} = -27.227137301601
x12=96.3421747038964x_{12} = 96.3421747038964
x13=17.8023636802631x_{13} = 17.8023636802631
x14=61.7846554839997x_{14} = -61.7846554839997
x15=21.9911508555068x_{15} = 21.9911508555068
x16=24.085542092727x_{16} = -24.085542092727
x17=49.218284815355x_{17} = -49.218284815355
x18=85.8701992079301x_{18} = -85.8701992079301
x19=90.058989411015x_{19} = -90.058989411015
x20=41.8879022211024x_{20} = -41.8879022211024
x21=10.4719311621712x_{21} = 10.4719311621712
x22=63.8790506550231x_{22} = 63.8790506550231
x23=15.7079545076246x_{23} = -15.7079545076246
x24=5.23527778575962x_{24} = -5.23527778575962
x25=70.1622359081638x_{25} = -70.1622359081638
x26=65.9734456972328x_{26} = -65.9734456972328
x27=98.4365698067999x_{27} = 98.4365698067999
x28=30.368729611737x_{28} = 30.368729611737
x29=9.42471036388476x_{29} = -9.42471036388476
x30=2.12078663718923x_{30} = -2.12078663718923
x31=81.681409005316x_{31} = -81.681409005316
x32=50.2654823738919x_{32} = 50.2654823738919
x33=76.4454212529685x_{33} = 76.4454212529685
x34=19.896756875795x_{34} = 19.896756875795
x35=26.1799376445792x_{35} = -26.1799376445792
x36=13.6135526376521x_{36} = -13.6135526376521
x37=24.0855452623157x_{37} = 24.0855452623157
x38=100.530964909652x_{38} = 100.530964909652
x39=92.1533844979053x_{39} = 92.1533844979053
x40=57.5958652673473x_{40} = -57.5958652673473
x41=87.9645943094219x_{41} = -87.9645943094219
x42=48.1710874540931x_{42} = -48.1710874540931
x43=70.1622359521803x_{43} = 70.1622359521803
x44=54.4542727228787x_{44} = -54.4542727228787
x45=79.5870139042346x_{45} = -79.5870139042346
x46=94.2477796144533x_{46} = -94.2477796144533
x47=78.5398163537613x_{47} = 78.5398163537613
x48=63.8790505909619x_{48} = -63.8790505909619
x49=21.9911462947484x_{49} = -21.9911462947484
x50=32.4631245673114x_{50} = 32.4631245673114
x51=11.5191427718506x_{51} = -11.5191427718506
x52=8.37747212994137x_{52} = 8.37747212994137
x53=30.3687283576656x_{53} = -30.3687283576656
x54=43.9822970077334x_{54} = 43.9822970077334
x55=94.2477796009343x_{55} = 94.2477796009343
x56=85.8701991883119x_{56} = 85.8701991883119
x57=59.6902604602192x_{57} = 59.6902604602192
x58=68.0678408029343x_{58} = -68.0678408029343
x59=35.6047170725548x_{59} = -35.6047170725548
x60=35.6047164088139x_{60} = 35.6047164088139
x61=4.18705493880793x_{61} = 4.18705493880793
x62=50.2654825409815x_{62} = -50.2654825409815
x63=92.1533845126959x_{63} = -92.1533845126959
x64=54.4542726015675x_{64} = 54.4542726015675
x65=37.6991115790348x_{65} = 37.6991115790348
x66=74.3510261524107x_{66} = 74.3510261524107
x67=90.0589893947998x_{67} = 90.0589893947998
x68=46.0766923709745x_{68} = -46.0766923709745
x69=39.7935067327793x_{69} = 39.7935067327793
x70=76.4454212217348x_{70} = -76.4454212217348
x71=39.7935071581621x_{71} = -39.7935071581621
x72=2.06502830067737x_{72} = 2.06502830067737
x73=89.0117918602067x_{73} = 89.0117918602067
x74=87.9645942916065x_{74} = 87.9645942916065
x75=6.28284303313608x_{75} = 6.28284303313608
x76=28.2743347168135x_{76} = 28.2743347168135
x77=43.9822972927808x_{77} = -43.9822972927808
x78=15.7079720282343x_{78} = 15.7079720282343
x79=72.2566310129999x_{79} = -72.2566310129999
x80=83.7758040849004x_{80} = 83.7758040849004
x81=52.3598774888714x_{81} = 52.3598774888714
x82=11.5192033538373x_{82} = 11.5192033538373
x83=68.0678408526234x_{83} = 68.0678408526234
x84=46.0766921343261x_{84} = 46.0766921343261
x85=77.4926188033379x_{85} = -77.4926188033379
x86=19.8967500696711x_{86} = -19.8967500696711
x87=26.1799399152503x_{87} = 26.1799399152503
x88=61.7846555571989x_{88} = 61.7846555571989
x89=48.1710872559938x_{89} = 48.1710872559938
x90=83.7758041065552x_{90} = -83.7758041065552
x91=56.5486677124597x_{91} = 56.5486677124597
x92=55.5014701572139x_{92} = -55.5014701572139
x93=33.5103220612365x_{93} = -33.5103220612365
x94=51.3126799317025x_{94} = -51.3126799317025
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 (5*x^4)*sin(3*x) + 8.
504sin(03)+85 \cdot 0^{4} \sin{\left(0 \cdot 3 \right)} + 8
Resultado:
f(0)=8f{\left(0 \right)} = 8
Punto:
(0, 8)
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
15x4cos(3x)+20x3sin(3x)=015 x^{4} \cos{\left(3 x \right)} + 20 x^{3} \sin{\left(3 x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=91.634635567103x_{1} = -91.634635567103
x2=63.3624651297861x_{2} = -63.3624651297861
x3=44.5158768953691x_{3} = 44.5158768953691
x4=40.3281224156889x_{4} = 40.3281224156889
x5=60.221238182616x_{5} = -60.221238182616
x6=73.8334462595067x_{6} = 73.8334462595067
x7=12.079417026695x_{7} = 12.079417026695
x8=49.7508149542794x_{8} = 49.7508149542794
x9=36.1406075887119x_{9} = -36.1406075887119
x10=75.9276753838356x_{10} = 75.9276753838356
x11=64.4095487013249x_{11} = 64.4095487013249
x12=53.9389119829474x_{12} = 53.9389119829474
x13=1.78467728039067x_{13} = -1.78467728039067
x14=2.76764306086567x_{14} = -2.76764306086567
x15=3.77827519433957x_{15} = 3.77827519433957
x16=49.7508149542794x_{16} = -49.7508149542794
x17=93.7289223191141x_{17} = 93.7289223191141
x18=75.9276753838356x_{18} = -75.9276753838356
x19=65.4566359175226x_{19} = -65.4566359175226
x20=21.4882064963395x_{20} = -21.4882064963395
x21=88.4932150522796x_{21} = 88.4932150522796
x22=31.9534263797684x_{22} = 31.9534263797684
x23=22.5344472736599x_{23} = 22.5344472736599
x24=82.2104134768321x_{24} = -82.2104134768321
x25=51.8448494812653x_{25} = 51.8448494812653
x26=14.1684434456615x_{26} = 14.1684434456615
x27=67.550820606457x_{27} = -67.550820606457
x28=47.6568120846336x_{28} = -47.6568120846336
x29=80.1161596550644x_{29} = 80.1161596550644
x30=78.0219134150581x_{30} = -78.0219134150581
x31=100.011809795649x_{31} = 100.011809795649
x32=18.3501348839456x_{32} = 18.3501348839456
x33=20.4420631577666x_{33} = 20.4420631577666
x34=86.3989416613461x_{34} = 86.3989416613461
x35=18.3501348839456x_{35} = -18.3501348839456
x36=66.5037266063558x_{36} = 66.5037266063558
x37=0x_{37} = 0
x38=5.83447607252139x_{38} = 5.83447607252139
x39=78.0219134150581x_{39} = 78.0219134150581
x40=7.9096484587492x_{40} = 7.9096484587492
x41=29.8600046009359x_{41} = 29.8600046009359
x42=31.9534263797684x_{42} = -31.9534263797684
x43=12.079417026695x_{43} = -12.079417026695
x44=95.8232138061131x_{44} = 95.8232138061131
x45=9.99259294922328x_{45} = -9.99259294922328
x46=90.5874940693044x_{46} = 90.5874940693044
x47=82.2104134768321x_{47} = 82.2104134768321
x48=51.8448494812653x_{48} = -51.8448494812653
x49=71.7392268216346x_{49} = 71.7392268216346
x50=5.83447607252139x_{50} = -5.83447607252139
x51=43.4689195888571x_{51} = 43.4689195888571
x52=71.7392268216346x_{52} = -71.7392268216346
x53=25.6736357826784x_{53} = -25.6736357826784
x54=36.1406075887119x_{54} = 36.1406075887119
x55=38.234330134717x_{55} = -38.234330134717
x56=23.5807726014381x_{56} = -23.5807726014381
x57=38.234330134717x_{57} = 38.234330134717
x58=27.7667291875486x_{58} = -27.7667291875486
x59=73.8334462595067x_{59} = -73.8334462595067
x60=14.1684434456615x_{60} = -14.1684434456615
x61=53.9389119829474x_{61} = -53.9389119829474
x62=13.1237193239869x_{62} = -13.1237193239869
x63=93.7289223191141x_{63} = -93.7289223191141
x64=87.4460776282981x_{64} = -87.4460776282981
x65=69.6450179434699x_{65} = -69.6450179434699
x66=43.4689195888571x_{66} = -43.4689195888571
x67=56.0329993263719x_{67} = -56.0329993263719
x68=26.7201570725466x_{68} = 26.7201570725466
x69=97.9175097243864x_{69} = 97.9175097243864
x70=97.9175097243864x_{70} = -97.9175097243864
x71=7.9096484587492x_{71} = -7.9096484587492
x72=95.8232138061131x_{72} = -95.8232138061131
x73=84.3046743156037x_{73} = 84.3046743156037
x74=34.0469676095731x_{74} = 34.0469676095731
x75=100.011809795649x_{75} = -100.011809795649
x76=58.1271088294339x_{76} = 58.1271088294339
x77=58.1271088294339x_{77} = -58.1271088294339
x78=84.3046743156037x_{78} = -84.3046743156037
x79=80.1161596550644x_{79} = -80.1161596550644
x80=3.77827519433957x_{80} = -3.77827519433957
x81=29.8600046009359x_{81} = -29.8600046009359
x82=56.0329993263719x_{82} = 56.0329993263719
x83=35.0937763570717x_{83} = -35.0937763570717
x84=16.2588365740921x_{84} = -16.2588365740921
x85=50.7978285049785x_{85} = -50.7978285049785
x86=34.0469676095731x_{86} = -34.0469676095731
x87=62.315385386479x_{87} = 62.315385386479
x88=60.221238182616x_{88} = 60.221238182616
x89=9.99259294922328x_{89} = 9.99259294922328
x90=45.5628452306873x_{90} = -45.5628452306873
x91=42.4219741262856x_{91} = 42.4219741262856
x92=89.5403538821935x_{92} = -89.5403538821935
x93=16.2588365740921x_{93} = 16.2588365740921
x94=27.7667291875486x_{94} = 27.7667291875486
x95=1.78467728039067x_{95} = 1.78467728039067
x96=21.4882064963395x_{96} = 21.4882064963395
Signos de extremos en los puntos:
(-91.63463556710299, 352502882.774754)

(-63.36246512978607, -80575329.3464298)

(44.5158768953691, 19626153.617958)

(40.32812241568886, 13217978.5642116)

(-60.22123818261599, 65744943.8717191)

(73.83344625950674, 148563384.43735)

(12.079417026694966, -105801.386583899)

(49.75081495427937, -30620676.205518)

(-36.14060758871191, -8524247.27036998)

(75.9276753838356, 166151202.06203)

(64.40954870132492, -86035553.1893984)

(53.93891198294738, -42310290.1652217)

(-1.7846772803906716, 48.6352438938571)

(-2.7676430608656735, -256.295044714754)

(3.7782751943395687, -952.855158790833)

(-49.75081495427937, 30620692.205518)

(93.72892231911408, -385851818.778314)

(-75.9276753838356, -166151186.06203)

(-65.45663591752259, -91768706.6093194)

(-21.4882064963395, -1063978.7911248)

(88.49321505227961, 306591860.100884)

(31.953426379768374, 5207900.12662698)

(22.53444727365992, -1287051.88610351)

(-82.21041347683207, -228360091.27821)

(51.84484948126533, -36111772.4828875)

(14.168443445661534, -200598.036368131)

(-67.550820606457, -104089735.311377)

(-47.65681208463359, 25781025.1444908)

(80.11615965506437, 205963554.862822)

(-78.02191341505808, -185256291.490013)

(100.01180979564857, -500191780.740036)

(18.350134883945593, -565428.212317855)

(20.44206315776662, -871250.559055239)

(86.39894166134607, 278581324.408907)

(-18.350134883945593, 565444.212317855)

(66.50372660635584, -97783736.8115913)

(0, 8)

(5.8344760725213884, -5640.3716615012)

(78.02191341505808, 185256307.490013)

(7.909648458749203, -19290.0895429007)

(29.860004600935945, 3970981.16650358)

(-31.953426379768374, -5207884.12662698)

(-12.079417026694966, 105817.386583899)

(95.82321380611309, -421512916.768012)

(-9.99259294922328, 49422.0765649696)

(90.58749406930437, 336663442.788779)

(82.21041347683207, 228360107.27821)

(-51.84484948126533, 36111788.4828875)

(71.73922682163465, 132410309.430682)

(-5.8344760725213884, 5656.3716615012)

(43.46891958885709, -17843538.6981349)

(-71.73922682163465, -132410293.430682)

(-25.673635782678396, -2169366.94774642)

(36.14060758871191, 8524263.27036998)

(-38.234330134716956, -10678732.5315033)

(-23.580772601438067, -1543500.34903306)

(38.234330134716956, 10678748.5315033)

(-27.766729187548563, -2968708.82293071)

(-73.83344625950674, -148563368.43735)

(-14.168443445661534, 200614.036368131)

(-53.93891198294738, 42310306.1652217)

(-13.12371932398686, -147551.724253833)

(-93.72892231911408, 385851834.778314)

(-87.44607762829814, 292335040.429235)

(-69.64501794346985, -117611724.812966)

(-43.46891958885709, 17843554.6981349)

(-56.03299932637194, 49274546.3973751)

(26.720157072546627, -2545567.64244689)

(97.9175097243864, -459590641.013344)

(-97.9175097243864, 459590657.013344)

(-7.909648458749203, 19306.0895429007)

(-95.82321380611309, 421512932.768012)

(84.30467431560369, 252535436.790166)

(34.046967609573116, 6713538.80770276)

(-100.01180979564857, 500191796.740036)

(58.1271088294339, -57065103.2804346)

(-58.1271088294339, 57065119.2804346)

(-84.30467431560369, -252535420.790166)

(-80.11615965506437, -205963538.862822)

(-3.7782751943395687, 968.855158790833)

(-29.860004600935945, -3970965.16650358)

(56.03299932637194, -49274530.3973751)

(-35.093776357071675, 7578402.24394453)

(-16.258836574092104, 348243.000943114)

(-50.79782850497848, -33281350.2965328)

(-34.046967609573116, -6713522.80770276)

(62.31538538647896, -75379232.1847793)

(60.22123818261599, -65744927.8717191)

(9.99259294922328, -49406.0765649696)

(-45.56284523068725, 21539104.0674156)

(42.421974126285555, 16185246.2978379)

(-89.54035388219354, 321363905.444071)

(16.258836574092104, -348227.000943114)

(27.766729187548563, 2968724.82293071)

(1.7846772803906716, -32.6352438938571)

(21.4882064963395, 1063994.7911248)


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=63.3624651297861x_{1} = -63.3624651297861
x2=12.079417026695x_{2} = 12.079417026695
x3=49.7508149542794x_{3} = 49.7508149542794
x4=36.1406075887119x_{4} = -36.1406075887119
x5=64.4095487013249x_{5} = 64.4095487013249
x6=53.9389119829474x_{6} = 53.9389119829474
x7=2.76764306086567x_{7} = -2.76764306086567
x8=3.77827519433957x_{8} = 3.77827519433957
x9=93.7289223191141x_{9} = 93.7289223191141
x10=75.9276753838356x_{10} = -75.9276753838356
x11=65.4566359175226x_{11} = -65.4566359175226
x12=21.4882064963395x_{12} = -21.4882064963395
x13=22.5344472736599x_{13} = 22.5344472736599
x14=82.2104134768321x_{14} = -82.2104134768321
x15=51.8448494812653x_{15} = 51.8448494812653
x16=14.1684434456615x_{16} = 14.1684434456615
x17=67.550820606457x_{17} = -67.550820606457
x18=78.0219134150581x_{18} = -78.0219134150581
x19=100.011809795649x_{19} = 100.011809795649
x20=18.3501348839456x_{20} = 18.3501348839456
x21=20.4420631577666x_{21} = 20.4420631577666
x22=66.5037266063558x_{22} = 66.5037266063558
x23=5.83447607252139x_{23} = 5.83447607252139
x24=7.9096484587492x_{24} = 7.9096484587492
x25=31.9534263797684x_{25} = -31.9534263797684
x26=95.8232138061131x_{26} = 95.8232138061131
x27=43.4689195888571x_{27} = 43.4689195888571
x28=71.7392268216346x_{28} = -71.7392268216346
x29=25.6736357826784x_{29} = -25.6736357826784
x30=38.234330134717x_{30} = -38.234330134717
x31=23.5807726014381x_{31} = -23.5807726014381
x32=27.7667291875486x_{32} = -27.7667291875486
x33=73.8334462595067x_{33} = -73.8334462595067
x34=13.1237193239869x_{34} = -13.1237193239869
x35=69.6450179434699x_{35} = -69.6450179434699
x36=26.7201570725466x_{36} = 26.7201570725466
x37=97.9175097243864x_{37} = 97.9175097243864
x38=58.1271088294339x_{38} = 58.1271088294339
x39=84.3046743156037x_{39} = -84.3046743156037
x40=80.1161596550644x_{40} = -80.1161596550644
x41=29.8600046009359x_{41} = -29.8600046009359
x42=56.0329993263719x_{42} = 56.0329993263719
x43=50.7978285049785x_{43} = -50.7978285049785
x44=34.0469676095731x_{44} = -34.0469676095731
x45=62.315385386479x_{45} = 62.315385386479
x46=60.221238182616x_{46} = 60.221238182616
x47=9.99259294922328x_{47} = 9.99259294922328
x48=16.2588365740921x_{48} = 16.2588365740921
x49=1.78467728039067x_{49} = 1.78467728039067
Puntos máximos de la función:
x49=91.634635567103x_{49} = -91.634635567103
x49=44.5158768953691x_{49} = 44.5158768953691
x49=40.3281224156889x_{49} = 40.3281224156889
x49=60.221238182616x_{49} = -60.221238182616
x49=73.8334462595067x_{49} = 73.8334462595067
x49=75.9276753838356x_{49} = 75.9276753838356
x49=1.78467728039067x_{49} = -1.78467728039067
x49=49.7508149542794x_{49} = -49.7508149542794
x49=88.4932150522796x_{49} = 88.4932150522796
x49=31.9534263797684x_{49} = 31.9534263797684
x49=47.6568120846336x_{49} = -47.6568120846336
x49=80.1161596550644x_{49} = 80.1161596550644
x49=86.3989416613461x_{49} = 86.3989416613461
x49=18.3501348839456x_{49} = -18.3501348839456
x49=78.0219134150581x_{49} = 78.0219134150581
x49=29.8600046009359x_{49} = 29.8600046009359
x49=12.079417026695x_{49} = -12.079417026695
x49=9.99259294922328x_{49} = -9.99259294922328
x49=90.5874940693044x_{49} = 90.5874940693044
x49=82.2104134768321x_{49} = 82.2104134768321
x49=51.8448494812653x_{49} = -51.8448494812653
x49=71.7392268216346x_{49} = 71.7392268216346
x49=5.83447607252139x_{49} = -5.83447607252139
x49=36.1406075887119x_{49} = 36.1406075887119
x49=38.234330134717x_{49} = 38.234330134717
x49=14.1684434456615x_{49} = -14.1684434456615
x49=53.9389119829474x_{49} = -53.9389119829474
x49=93.7289223191141x_{49} = -93.7289223191141
x49=87.4460776282981x_{49} = -87.4460776282981
x49=43.4689195888571x_{49} = -43.4689195888571
x49=56.0329993263719x_{49} = -56.0329993263719
x49=97.9175097243864x_{49} = -97.9175097243864
x49=7.9096484587492x_{49} = -7.9096484587492
x49=95.8232138061131x_{49} = -95.8232138061131
x49=84.3046743156037x_{49} = 84.3046743156037
x49=34.0469676095731x_{49} = 34.0469676095731
x49=100.011809795649x_{49} = -100.011809795649
x49=58.1271088294339x_{49} = -58.1271088294339
x49=3.77827519433957x_{49} = -3.77827519433957
x49=35.0937763570717x_{49} = -35.0937763570717
x49=16.2588365740921x_{49} = -16.2588365740921
x49=45.5628452306873x_{49} = -45.5628452306873
x49=42.4219741262856x_{49} = 42.4219741262856
x49=89.5403538821935x_{49} = -89.5403538821935
x49=27.7667291875486x_{49} = 27.7667291875486
x49=21.4882064963395x_{49} = 21.4882064963395
Decrece en los intervalos
[100.011809795649,)\left[100.011809795649, \infty\right)
Crece en los intervalos
(,84.3046743156037]\left(-\infty, -84.3046743156037\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
15x2(3x2sin(3x)+8xcos(3x)+4sin(3x))=015 x^{2} \left(- 3 x^{2} \sin{\left(3 x \right)} + 8 x \cos{\left(3 x \right)} + 4 \sin{\left(3 x \right)}\right) = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=19.9412133653678x_{1} = 19.9412133653678
x2=13.6781981805575x_{2} = 13.6781981805575
x3=44.0024872219432x_{3} = -44.0024872219432
x4=48.1895248129449x_{4} = -48.1895248129449
x5=31.4441657573793x_{5} = -31.4441657573793
x6=37.7226584907908x_{6} = 37.7226584907908
x7=68.0808942713035x_{7} = -68.0808942713035
x8=57.611289573061x_{8} = -57.611289573061
x9=2.41475995036756x_{9} = 2.41475995036756
x10=67.0339005068352x_{10} = -67.0339005068352
x11=9.51713400362032x_{11} = -9.51713400362032
x12=94.2572089677385x_{12} = -94.2572089677385
x13=85.8805480368887x_{13} = -85.8805480368887
x14=4.38184751638645x_{14} = 4.38184751638645
x15=11.5952515138254x_{15} = -11.5952515138254
x16=26.2137969781228x_{16} = -26.2137969781228
x17=35.629644412359x_{17} = -35.629644412359
x18=32.4904557312044x_{18} = 32.4904557312044
x19=77.5040857387186x_{19} = -77.5040857387186
x20=39.8158173819729x_{20} = -39.8158173819729
x21=54.4705856582764x_{21} = 54.4705856582764
x22=0x_{22} = 0
x23=63.8929592480062x_{23} = 63.8929592480062
x24=7.44759282756602x_{24} = -7.44759282756602
x25=29.3517790648431x_{25} = -29.3517790648431
x26=61.7990351572089x_{26} = -61.7990351572089
x27=52.3768421785014x_{27} = 52.3768421785014
x28=13.6781981805575x_{28} = -13.6781981805575
x29=3.38433916342539x_{29} = -3.38433916342539
x30=52.3768421785014x_{30} = -52.3768421785014
x31=48.1895248129449x_{31} = 48.1895248129449
x32=50.2831528816126x_{32} = -50.2831528816126
x33=73.3159503317116x_{33} = -73.3159503317116
x34=83.786411515323x_{34} = -83.786411515323
x35=46.0959662934791x_{35} = 46.0959662934791
x36=27.2596991353031x_{36} = 27.2596991353031
x37=63.8929592480062x_{37} = -63.8929592480062
x38=98.4455980861048x_{38} = 98.4455980861048
x39=81.6922882431236x_{39} = -81.6922882431236
x40=22.0314092220231x_{40} = 22.0314092220231
x41=41.9090994669373x_{41} = 41.9090994669373
x42=76.4570451662999x_{42} = -76.4570451662999
x43=44.0024872219432x_{43} = 44.0024872219432
x44=33.5368021292213x_{44} = 33.5368021292213
x45=17.8519896631247x_{45} = -17.8519896631247
x46=70.1749000278588x_{46} = 70.1749000278588
x47=39.8158173819729x_{47} = 39.8158173819729
x48=41.9090994669373x_{48} = -41.9090994669373
x49=118.340833990081x_{49} = -118.340833990081
x50=68.0808942713035x_{50} = 68.0808942713035
x51=83.786411515323x_{51} = 83.786411515323
x52=8.48092656630217x_{52} = 8.48092656630217
x53=100.539805171869x_{53} = 100.539805171869
x54=57.611289573061x_{54} = 57.611289573061
x55=72.2689283294871x_{55} = 72.2689283294871
x56=61.7990351572089x_{56} = 61.7990351572089
x57=30.3979379987071x_{57} = 30.3979379987071
x58=4.38184751638645x_{58} = -4.38184751638645
x59=79.59817926507x_{59} = -79.59817926507
x60=15.7641169868267x_{60} = -15.7641169868267
x61=22.0314092220231x_{61} = -22.0314092220231
x62=92.1630280729278x_{62} = -92.1630280729278
x63=65.9869132033459x_{63} = 65.9869132033459
x64=50.2831528816126x_{64} = 50.2831528816126
x65=74.3629772737418x_{65} = 74.3629772737418
x66=26.2137969781228x_{66} = 26.2137969781228
x67=92.1630280729278x_{67} = 92.1630280729278
x68=7.44759282756602x_{68} = 7.44759282756602
x69=6.41837429605925x_{69} = 6.41837429605925
x70=15.7641169868267x_{70} = 15.7641169868267
x71=24.1223274832976x_{71} = 24.1223274832976
x72=46.0959662934791x_{72} = -46.0959662934791
x73=1.49638814980168x_{73} = -1.49638814980168
x74=33.5368021292213x_{74} = -33.5368021292213
x75=23.0767901828642x_{75} = -23.0767901828642
x76=72.2689283294871x_{76} = -72.2689283294871
x77=24.1223274832976x_{77} = -24.1223274832976
x78=81.6922882431236x_{78} = 81.6922882431236
x79=90.0688571343282x_{79} = 90.0688571343282
x80=59.7051440681381x_{80} = -59.7051440681381
x81=65.9869132033459x_{81} = -65.9869132033459
x82=59.7051440681381x_{82} = 59.7051440681381
x83=70.1749000278588x_{83} = -70.1749000278588
x84=94.2572089677385x_{84} = 94.2572089677385
x85=28.3056965337542x_{85} = 28.3056965337542
x86=37.7226584907908x_{86} = -37.7226584907908
x87=76.4570451662999x_{87} = 76.4570451662999
x88=19.9412133653678x_{88} = -19.9412133653678
x89=87.9746968624141x_{89} = -87.9746968624141
x90=55.5174758048981x_{90} = -55.5174758048981
x91=85.8805480368887x_{91} = 85.8805480368887
x92=17.8519896631247x_{92} = 17.8519896631247
x93=87.9746968624141x_{93} = 87.9746968624141
x94=90.0688571343282x_{94} = -90.0688571343282
x95=9.51713400362032x_{95} = 9.51713400362032
x96=78.5511304932684x_{96} = 78.5511304932684
x97=96.3513991699991x_{97} = 96.3513991699991
x98=99.4927006400028x_{98} = -99.4927006400028

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
[78.5511304932684,)\left[78.5511304932684, \infty\right)
Convexa en los intervalos
(,118.340833990081]\left(-\infty, -118.340833990081\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
limx(5x4sin(3x)+8)=,\lim_{x \to -\infty}\left(5 x^{4} \sin{\left(3 x \right)} + 8\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(5x4sin(3x)+8)=,\lim_{x \to \infty}\left(5 x^{4} \sin{\left(3 x \right)} + 8\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 (5*x^4)*sin(3*x) + 8, 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(5x4sin(3x)+8x)y = x \lim_{x \to -\infty}\left(\frac{5 x^{4} \sin{\left(3 x \right)} + 8}{x}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=xlimx(5x4sin(3x)+8x)y = x \lim_{x \to \infty}\left(\frac{5 x^{4} \sin{\left(3 x \right)} + 8}{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:
5x4sin(3x)+8=5x4sin(3x)+85 x^{4} \sin{\left(3 x \right)} + 8 = - 5 x^{4} \sin{\left(3 x \right)} + 8
- No
5x4sin(3x)+8=5x4sin(3x)85 x^{4} \sin{\left(3 x \right)} + 8 = 5 x^{4} \sin{\left(3 x \right)} - 8
- No
es decir, función
no es
par ni impar
Gráfico
Gráfico de la función y = 5*x^4*sin(3*x)+8