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Gráfico de la función y = (((sin(x))*(x)+cos((x)^2))/10)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src]
                     / 2\
       sin(x)*x + cos\x /
f(x) = ------------------
               10        
f(x)=xsin(x)+cos(x2)10f{\left(x \right)} = \frac{x \sin{\left(x \right)} + \cos{\left(x^{2} \right)}}{10}
f = (x*sin(x) + cos(x^2))/10
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:
xsin(x)+cos(x2)10=0\frac{x \sin{\left(x \right)} + \cos{\left(x^{2} \right)}}{10} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=25.1507585059292x_{1} = -25.1507585059292
x2=62.8453589178694x_{2} = -62.8453589178694
x3=37.6760309699686x_{3} = -37.6760309699686
x4=78.5277836460506x_{4} = -78.5277836460506
x5=87.970350365565x_{5} = 87.970350365565
x6=43.9763165099716x_{6} = -43.9763165099716
x7=12.5051781854023x_{7} = -12.5051781854023
x8=62.8453589178694x_{8} = 62.8453589178694
x9=50.2505527909721x_{9} = 50.2505527909721
x10=75.3974270561651x_{10} = 75.3974270561651
x11=34.56855132472x_{11} = 34.56855132472
x12=62.8159328801266x_{12} = -62.8159328801266
x13=6.24975963032938x_{13} = -6.24975963032938
x14=65.9762059623288x_{14} = -65.9762059623288
x15=47.1159905361563x_{15} = 47.1159905361563
x16=69.1136341503526x_{16} = 69.1136341503526
x17=87.970350365565x_{17} = -87.970350365565
x18=75.3974270561651x_{18} = -75.3974270561651
x19=6.42472201291267x_{19} = -6.42472201291267
x20=37.6760309699686x_{20} = 37.6760309699686
x21=91.1109658407088x_{21} = -91.1109658407088
x22=40.829829507478x_{22} = 40.829829507478
x23=84.8264287170751x_{23} = 84.8264287170751
x24=69.1136341503526x_{24} = -69.1136341503526
x25=40.829829507478x_{25} = -40.829829507478
x26=22.0173152631452x_{26} = 22.0173152631452
x27=56.5417666263814x_{27} = 56.5417666263814
x28=78.5519175863755x_{28} = -78.5519175863755
x29=69.1010659379897x_{29} = 69.1010659379897
x30=84.8264287170751x_{30} = -84.8264287170751
x31=53.4181797391065x_{31} = 53.4181797391065
x32=34.56855132472x_{32} = -34.56855132472
x33=6.24975963032938x_{33} = 6.24975963032938
x34=28.2754817492699x_{34} = -28.2754817492699
x35=18.8716763254854x_{35} = 18.8716763254854
x36=65.9762059623288x_{36} = 65.9762059623288
x37=37.7085443838676x_{37} = 37.7085443838676
x38=12.5051781854023x_{38} = 12.5051781854023
x39=15.7053088016692x_{39} = -15.7053088016692
x40=31.3946181535251x_{40} = 31.3946181535251
x41=47.1159905361563x_{41} = -47.1159905361563
x42=100.536176798472x_{42} = 100.536176798472
x43=78.5400000063693x_{43} = 78.5400000063693
x44=28.2754817492699x_{44} = 28.2754817492699
x45=25.1507585059292x_{45} = 25.1507585059292
x46=9.44972955620159x_{46} = 9.44972955620159
x47=59.6969512155175x_{47} = -59.6969512155175
x48=56.5417666263814x_{48} = -56.5417666263814
x49=9.44972955620159x_{49} = -9.44972955620159
x50=91.1109658407088x_{50} = 91.1109658407088
x51=6.1227836207913x_{51} = 6.1227836207913
x52=59.6969512155175x_{52} = 59.6969512155175
x53=2.92263258416456x_{53} = 2.92263258416456
x54=81.6786396314427x_{54} = -81.6786396314427
x55=94.2485195342584x_{55} = -94.2485195342584
x56=72.2650767518132x_{56} = 72.2650767518132
x57=31.3946181535251x_{57} = -31.3946181535251
x58=43.9763165099716x_{58} = 43.9763165099716
x59=15.7053088016692x_{59} = 15.7053088016692
x60=103.665787844547x_{60} = -103.665787844547
x61=94.2485195342584x_{61} = 94.2485195342584
x62=18.8716763254854x_{62} = -18.8716763254854
x63=22.0173152631452x_{63} = -22.0173152631452
x64=81.6786396314427x_{64} = 81.6786396314427
x65=62.8159328801266x_{65} = 62.8159328801266
x66=53.4181797391065x_{66} = -53.4181797391065
x67=2.92263258416456x_{67} = -2.92263258416456
x68=97.3833730399253x_{68} = -97.3833730399253
x69=97.3833730399253x_{69} = 97.3833730399253
x70=69.1284624724437x_{70} = -69.1284624724437
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(x)*x + cos(x^2))/10.
0sin(0)+cos(02)10\frac{0 \sin{\left(0 \right)} + \cos{\left(0^{2} \right)}}{10}
Resultado:
f(0)=110f{\left(0 \right)} = \frac{1}{10}
Punto:
(0, 1/10)
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
xsin(x2)5+xcos(x)10+sin(x)10=0- \frac{x \sin{\left(x^{2} \right)}}{5} + \frac{x \cos{\left(x \right)}}{10} + \frac{\sin{\left(x \right)}}{10} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=48.7022477806709x_{1} = -48.7022477806709
x2=7.71735614274688x_{2} = 7.71735614274688
x3=72.1971212313864x_{3} = -72.1971212313864
x4=10.3177119071094x_{4} = -10.3177119071094
x5=65.6966431361821x_{5} = 65.6966431361821
x6=97.9167562155769x_{6} = -97.9167562155769
x7=86.6322809608577x_{7} = 86.6322809608577
x8=106.330315020759x_{8} = -106.330315020759
x9=34.6044873742924x_{9} = -34.6044873742924
x10=92.8472387034767x_{10} = -92.8472387034767
x11=16.3543910595232x_{11} = 16.3543910595232
x12=60.2075059445502x_{12} = 60.2075059445502
x13=18.4324293780352x_{13} = 18.4324293780352
x14=80.8924111129607x_{14} = -80.8924111129607
x15=66.6468706982917x_{15} = 66.6468706982917
x16=4.01707375066121x_{16} = -4.01707375066121
x17=22.2203616723701x_{17} = 22.2203616723701
x18=55.9619856415426x_{18} = -55.9619856415426
x19=7.71735614274688x_{19} = -7.71735614274688
x20=3.15447101965658x_{20} = 3.15447101965658
x21=65.6488702899613x_{21} = -65.6488702899613
x22=70.4545118097616x_{22} = -70.4545118097616
x23=70.295998160484x_{23} = 70.295998160484
x24=6.18144670783899x_{24} = 6.18144670783899
x25=4.70140607837036x_{25} = -4.70140607837036
x26=86.1412265197624x_{26} = -86.1412265197624
x27=94.0709995413408x_{27} = 94.0709995413408
x28=4.3058416030361x_{28} = -4.3058416030361
x29=48.2508666158054x_{29} = 48.2508666158054
x30=77.0962790585706x_{30} = -77.0962790585706
x31=10.0034367732019x_{31} = -10.0034367732019
x32=42.1325230941268x_{32} = 42.1325230941268
x33=5.84199823326316x_{33} = -5.84199823326316
x34=45.8460449466837x_{34} = -45.8460449466837
x35=8.30368499290797x_{35} = 8.30368499290797
x36=95.662827587978x_{36} = -95.662827587978
x37=81.6644219239386x_{37} = -81.6644219239386
x38=2.45419750426626x_{38} = -2.45419750426626
x39=22.0787348910193x_{39} = -22.0787348910193
x40=31.8131873761686x_{40} = -31.8131873761686
x41=100.798885220958x_{41} = -100.798885220958
x42=84.0958001656817x_{42} = 84.0958001656817
x43=0x_{43} = 0
x44=33.9952636190527x_{44} = -33.9952636190527
x45=1.70832357549316x_{45} = -1.70832357549316
x46=57.8170597783129x_{46} = 57.8170597783129
x47=20.1270039011068x_{47} = 20.1270039011068
x48=65.584434565761x_{48} = -65.584434565761
x49=8.12706120989409x_{49} = 8.12706120989409
x50=64.4208447039076x_{50} = -64.4208447039076
x51=13.6038254362701x_{51} = -13.6038254362701
x52=39.8342064746482x_{52} = -39.8342064746482
x53=12.0389778255654x_{53} = 12.0389778255654
x54=78.2123503328964x_{54} = 78.2123503328964
x55=42.8674752903881x_{55} = 42.8674752903881
x56=111.580058308936x_{56} = -111.580058308936
x57=27.3388583553737x_{57} = -27.3388583553737
x58=3.46694020065127x_{58} = -3.46694020065127
x59=25.3259185229567x_{59} = 25.3259185229567
x60=84.0208851272327x_{60} = 84.0208851272327
x61=28.2018358131537x_{61} = 28.2018358131537
x62=22.6894868601214x_{62} = 22.6894868601214
x63=0.91227760452467x_{63} = 0.91227760452467
x64=41.2321150095001x_{64} = 41.2321150095001
x65=15.6372846856132x_{65} = -15.6372846856132
x66=89.4346173963249x_{66} = -89.4346173963249
x67=19.7457836379102x_{67} = -19.7457836379102
x68=28.1276895911551x_{68} = 28.1276895911551
x69=27.7511836426124x_{69} = -27.7511836426124
x70=86.1972744923x_{70} = 86.1972744923
x71=80.0750561846556x_{71} = 80.0750561846556
x72=65.4402907264533x_{72} = 65.4402907264533
x73=17.8064964905354x_{73} = -17.8064964905354
x74=30.1296454562873x_{74} = 30.1296454562873
x75=54.6867749274687x_{75} = -54.6867749274687
x76=74.2937260357796x_{76} = 74.2937260357796
x77=3.15447101965658x_{77} = -3.15447101965658
Signos de extremos en los puntos:
(-48.70224778067086, -4.97008343949975)

(7.717356142746883, 0.665422837563182)

(-72.19712123138642, 0.342712794353287)

(-10.31771190710938, -0.71003624645981)

(65.69664313618212, 1.88315439087601)

(-97.91675621557687, -4.83783961509656)

(86.63228096085766, -8.51740179464128)

(-106.33031502075858, -5.03602693432363)

(-34.60448737429242, -0.249066452121543)

(-92.84723870347672, -9.05079668614192)

(16.35439105952323, -1.0759544466602)

(60.20750594455023, -2.88732472560803)

(18.432429378035238, -0.657265939645225)

(-80.89241111296074, -5.83426382771044)

(66.64687069829165, -4.06469921030841)

(-4.01707375066121, -0.399393345815697)

(22.220361672370093, -0.591929182276222)

(-55.96198564154261, -3.1892046274228)

(-7.717356142746883, 0.665422837563182)

(3.1544710196565804, -0.0905491063721037)

(-65.64887028996131, 2.18177312687303)

(-70.4545118097616, 6.95704685710632)

(70.29599816048396, 6.40412889139749)

(6.181446707838987, 0.0244364605265608)

(-4.701406078370362, -0.569484919699594)

(-86.14122651976237, -8.24167870962079)

(94.07099954134081, -1.74144012947284)

(-4.305841603036097, -0.300232760483891)

(48.25086661580537, -4.4550811700269)

(-77.09627905857064, 7.74712119662881)

(-10.003436773201935, -0.457582970791433)

(42.13252309412676, -4.14923950338143)

(-5.841998233263159, -0.340416871699648)

(-45.8460449466837, 4.29018190439188)

(8.303684992907966, 0.846470612909434)

(-95.66282758797803, 9.35083257833794)

(-81.66442192393863, -0.225329955993049)

(-2.454197504266257, 0.252361652074853)

(-22.07873489101931, -0.279731177138947)

(-31.813187376168614, 1.31925116410956)

(-100.79888522095813, 2.7559495602951)

(84.09580016568168, 5.49761397559051)

      1  
(0, --)
      10 

(-33.99526361905273, 1.90324715072548)

(-1.7083235754931594, 0.0717004644994605)

(57.81705977831294, 5.61810795016586)

(20.12700390110677, 1.82814737174093)

(-65.58443456576097, 2.39863993743084)

(8.12706120989409, 0.682877443525778)

(-64.42084470390765, 6.34101820151746)

(-13.60382543627007, 1.07561586835187)

(-39.83420647464824, 3.26920109683717)

(12.0389778255654, -0.51474384123171)

(78.21235033289636, 2.42746565514769)

(42.86747529038811, -3.94655730376977)

(-111.58005830893566, -11.2420049305561)

(-27.338858355373734, 2.29639527630697)

(-3.466940200651274, -0.0253919557783296)

(25.325918522956723, 0.573120397912599)

(84.02088512723267, 5.94574352155722)

(28.20183581315366, 0.117526810966497)

(22.689486860121427, -1.36703465001299)

(0.91227760452467, 0.139473334808921)

(41.23211500950011, -1.66141046278679)

(-15.637284685613174, 0.197234154489326)

(-89.43461739632491, 8.99793247906628)

(-19.745783637910193, 1.6364251730452)

(28.127689591155107, 0.498057227195239)

(-27.75118364261237, 1.29592061435408)

(86.19727449229995, -8.55327399499498)

(80.07505618465555, -8.10241551414927)

(65.44029072645333, 3.23558389954278)

(-17.8064964905354, -1.63576746654434)

(30.129645456287317, -2.99105982350954)

(-54.68677492746872, -5.1397748113923)

(74.29372603577959, -6.73377873236178)

(-3.1544710196565804, -0.0905491063721037)


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=48.7022477806709x_{1} = -48.7022477806709
x2=7.71735614274688x_{2} = 7.71735614274688
x3=72.1971212313864x_{3} = -72.1971212313864
x4=86.6322809608577x_{4} = 86.6322809608577
x5=106.330315020759x_{5} = -106.330315020759
x6=34.6044873742924x_{6} = -34.6044873742924
x7=16.3543910595232x_{7} = 16.3543910595232
x8=80.8924111129607x_{8} = -80.8924111129607
x9=4.01707375066121x_{9} = -4.01707375066121
x10=22.2203616723701x_{10} = 22.2203616723701
x11=55.9619856415426x_{11} = -55.9619856415426
x12=7.71735614274688x_{12} = -7.71735614274688
x13=3.15447101965658x_{13} = 3.15447101965658
x14=70.295998160484x_{14} = 70.295998160484
x15=4.70140607837036x_{15} = -4.70140607837036
x16=94.0709995413408x_{16} = 94.0709995413408
x17=48.2508666158054x_{17} = 48.2508666158054
x18=42.1325230941268x_{18} = 42.1325230941268
x19=5.84199823326316x_{19} = -5.84199823326316
x20=45.8460449466837x_{20} = -45.8460449466837
x21=95.662827587978x_{21} = -95.662827587978
x22=81.6644219239386x_{22} = -81.6644219239386
x23=22.0787348910193x_{23} = -22.0787348910193
x24=84.0958001656817x_{24} = 84.0958001656817
x25=0x_{25} = 0
x26=1.70832357549316x_{26} = -1.70832357549316
x27=20.1270039011068x_{27} = 20.1270039011068
x28=65.584434565761x_{28} = -65.584434565761
x29=8.12706120989409x_{29} = 8.12706120989409
x30=64.4208447039076x_{30} = -64.4208447039076
x31=13.6038254362701x_{31} = -13.6038254362701
x32=39.8342064746482x_{32} = -39.8342064746482
x33=78.2123503328964x_{33} = 78.2123503328964
x34=42.8674752903881x_{34} = 42.8674752903881
x35=111.580058308936x_{35} = -111.580058308936
x36=84.0208851272327x_{36} = 84.0208851272327
x37=28.2018358131537x_{37} = 28.2018358131537
x38=41.2321150095001x_{38} = 41.2321150095001
x39=27.7511836426124x_{39} = -27.7511836426124
x40=86.1972744923x_{40} = 86.1972744923
x41=80.0750561846556x_{41} = 80.0750561846556
x42=65.4402907264533x_{42} = 65.4402907264533
x43=17.8064964905354x_{43} = -17.8064964905354
x44=30.1296454562873x_{44} = 30.1296454562873
x45=74.2937260357796x_{45} = 74.2937260357796
x46=3.15447101965658x_{46} = -3.15447101965658
Puntos máximos de la función:
x46=10.3177119071094x_{46} = -10.3177119071094
x46=65.6966431361821x_{46} = 65.6966431361821
x46=97.9167562155769x_{46} = -97.9167562155769
x46=92.8472387034767x_{46} = -92.8472387034767
x46=60.2075059445502x_{46} = 60.2075059445502
x46=18.4324293780352x_{46} = 18.4324293780352
x46=66.6468706982917x_{46} = 66.6468706982917
x46=65.6488702899613x_{46} = -65.6488702899613
x46=70.4545118097616x_{46} = -70.4545118097616
x46=6.18144670783899x_{46} = 6.18144670783899
x46=86.1412265197624x_{46} = -86.1412265197624
x46=4.3058416030361x_{46} = -4.3058416030361
x46=77.0962790585706x_{46} = -77.0962790585706
x46=10.0034367732019x_{46} = -10.0034367732019
x46=8.30368499290797x_{46} = 8.30368499290797
x46=2.45419750426626x_{46} = -2.45419750426626
x46=31.8131873761686x_{46} = -31.8131873761686
x46=100.798885220958x_{46} = -100.798885220958
x46=33.9952636190527x_{46} = -33.9952636190527
x46=57.8170597783129x_{46} = 57.8170597783129
x46=12.0389778255654x_{46} = 12.0389778255654
x46=27.3388583553737x_{46} = -27.3388583553737
x46=3.46694020065127x_{46} = -3.46694020065127
x46=25.3259185229567x_{46} = 25.3259185229567
x46=22.6894868601214x_{46} = 22.6894868601214
x46=0.91227760452467x_{46} = 0.91227760452467
x46=15.6372846856132x_{46} = -15.6372846856132
x46=89.4346173963249x_{46} = -89.4346173963249
x46=19.7457836379102x_{46} = -19.7457836379102
x46=28.1276895911551x_{46} = 28.1276895911551
x46=54.6867749274687x_{46} = -54.6867749274687
Decrece en los intervalos
[94.0709995413408,)\left[94.0709995413408, \infty\right)
Crece en los intervalos
(,111.580058308936]\left(-\infty, -111.580058308936\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
4x2cos(x2)xsin(x)2sin(x2)+2cos(x)10=0\frac{- 4 x^{2} \cos{\left(x^{2} \right)} - x \sin{\left(x \right)} - 2 \sin{\left(x^{2} \right)} + 2 \cos{\left(x \right)}}{10} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=2.1595469388602x_{1} = -2.1595469388602
x2=6.51352412038434x_{2} = -6.51352412038434
x3=14.013189373673x_{3} = 14.013189373673
x4=1.39637138373029x_{4} = -1.39637138373029
x5=12.9643145360403x_{5} = 12.9643145360403
x6=67.8528384507446x_{6} = -67.8528384507446
x7=8.94977808971084x_{7} = -8.94977808971084
x8=27.9968738528445x_{8} = 27.9968738528445
x9=7.20192060672632x_{9} = -7.20192060672632
x10=34.2088671098253x_{10} = 34.2088671098253
x11=47.8727005114214x_{11} = -47.8727005114214
x12=9.29464127489755x_{12} = -9.29464127489755
x13=90.073111997569x_{13} = -90.073111997569
x14=22.3145878522539x_{14} = 22.3145878522539
x15=76.0814468713479x_{15} = 76.0814468713479
x16=56.0919540544261x_{16} = 56.0919540544261
x17=17.8573738556617x_{17} = -17.8573738556617
x18=53.5709403751886x_{18} = -53.5709403751886
x19=18.1187088667744x_{19} = 18.1187088667744
x20=63.9681799581795x_{20} = 63.9681799581795
x21=37.0735942819773x_{21} = -37.0735942819773
x22=36.0857815972618x_{22} = 36.0857815972618
x23=2.1595469388602x_{23} = 2.1595469388602
x24=20.2482348999244x_{24} = 20.2482348999244
x25=45.964403359661x_{25} = -45.964403359661
x26=5.4686909770366x_{26} = -5.4686909770366
x27=72.7246367692711x_{27} = 72.7246367692711
x28=9.29464127489755x_{28} = 9.29464127489755
x29=1.39637138373029x_{29} = 1.39637138373029
x30=20.9342388285384x_{30} = -20.9342388285384
x31=66.1650216073689x_{31} = 66.1650216073689
x32=95.4578020782042x_{32} = -95.4578020782042
x33=49.454284737491x_{33} = -49.454284737491
x34=75.8332826003072x_{34} = -75.8332826003072
x35=61.8710545591208x_{35} = 61.8710545591208
x36=40.1647108958762x_{36} = 40.1647108958762
x37=70.8205922213983x_{37} = -70.8205922213983
x38=92.295346745483x_{38} = -92.295346745483
x39=36.3893997738794x_{39} = -36.3893997738794
x40=10.2597748154338x_{40} = 10.2597748154338
x41=69.7703075627013x_{41} = -69.7703075627013
x42=79.5533522508038x_{42} = 79.5533522508038
x43=46.0326993331084x_{43} = 46.0326993331084
x44=80.1827059156383x_{44} = 80.1827059156383
x45=33.9322679198802x_{45} = 33.9322679198802
x46=81.8309503456342x_{46} = 81.8309503456342
x47=32.1250427380947x_{47} = 32.1250427380947
x48=42.9615066945547x_{48} = -42.9615066945547
x49=57.7476992851973x_{49} = -57.7476992851973
x50=21.7443000958436x_{50} = -21.7443000958436
x51=29.8960748148361x_{51} = -29.8960748148361
x52=85.7673690159086x_{52} = -85.7673690159086
x53=20.0924681286551x_{53} = -20.0924681286551
x54=12.086144517777x_{54} = -12.086144517777
x55=97.7504729546357x_{55} = -97.7504729546357
x56=94.2155520115741x_{56} = 94.2155520115741
x57=70.1295973687977x_{57} = 70.1295973687977
x58=5.4686909770366x_{58} = 5.4686909770366
x59=73.1553538359721x_{59} = 73.1553538359721
x60=81.638772008703x_{60} = -81.638772008703
x61=6.51352412038434x_{61} = 6.51352412038434
x62=3.76330573841933x_{62} = -3.76330573841933
x63=32.754343789681x_{63} = -32.754343789681
x64=65.855670478107x_{64} = -65.855670478107
x65=8.02760408197227x_{65} = -8.02760408197227
x66=60.250415242516x_{66} = 60.250415242516
x67=3.31805703287389x_{67} = 3.31805703287389
x68=32.9934825995173x_{68} = 32.9934825995173
x69=85.492184535196x_{69} = -85.492184535196
x70=23.7471530705841x_{70} = -23.7471530705841
x71=4.51612042536184x_{71} = -4.51612042536184
x72=15.9028010660491x_{72} = 15.9028010660491
x73=50.5848670848442x_{73} = -50.5848670848442
x74=6.26651777484289x_{74} = 6.26651777484289
x75=3.31805703287389x_{75} = -3.31805703287389
x76=98.4390187617957x_{76} = -98.4390187617957
x77=4.16458939539259x_{77} = 4.16458939539259
x78=58.2352568102273x_{78} = 58.2352568102273
x79=31.9778852603693x_{79} = -31.9778852603693
x80=54.1251550547437x_{80} = 54.1251550547437
x81=0.506915362571624x_{81} = 0.506915362571624
x82=33.7929568159523x_{82} = -33.7929568159523
x83=16.2929297703181x_{83} = 16.2929297703181
x84=16.0013875517924x_{84} = -16.0013875517924
x85=7.82544031805579x_{85} = -7.82544031805579

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
[80.1827059156383,)\left[80.1827059156383, \infty\right)
Convexa en los intervalos
(,97.7504729546357]\left(-\infty, -97.7504729546357\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=limx(xsin(x)+cos(x2)10)y = \lim_{x \to -\infty}\left(\frac{x \sin{\left(x \right)} + \cos{\left(x^{2} \right)}}{10}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=limx(xsin(x)+cos(x2)10)y = \lim_{x \to \infty}\left(\frac{x \sin{\left(x \right)} + \cos{\left(x^{2} \right)}}{10}\right)
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función (sin(x)*x + cos(x^2))/10, 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(xsin(x)+cos(x2)10x)y = x \lim_{x \to -\infty}\left(\frac{x \sin{\left(x \right)} + \cos{\left(x^{2} \right)}}{10 x}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=xlimx(xsin(x)+cos(x2)10x)y = x \lim_{x \to \infty}\left(\frac{x \sin{\left(x \right)} + \cos{\left(x^{2} \right)}}{10 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:
xsin(x)+cos(x2)10=xsin(x)10+cos(x2)10\frac{x \sin{\left(x \right)} + \cos{\left(x^{2} \right)}}{10} = \frac{x \sin{\left(x \right)}}{10} + \frac{\cos{\left(x^{2} \right)}}{10}
- No
xsin(x)+cos(x2)10=xsin(x)10cos(x2)10\frac{x \sin{\left(x \right)} + \cos{\left(x^{2} \right)}}{10} = - \frac{x \sin{\left(x \right)}}{10} - \frac{\cos{\left(x^{2} \right)}}{10}
- No
es decir, función
no es
par ni impar