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

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

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
                 / 2\
f(x) = cos(x)*sin\x /
f(x)=sin⁡(x2)cos⁡(x)f{\left(x \right)} = \sin{\left(x^{2} \right)} \cos{\left(x \right)} 
f = sin(x^2)*cos(x)
Gráfico de la función
02468-8-6-4-2-10102-2
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:
sin⁡(x2)cos⁡(x)=0\sin{\left(x^{2} \right)} \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=14.1371669411541x_{1} = 14.1371669411541
x2=1.77245385090552x_{2} = 1.77245385090552
x3=−29.8172889607005x_{3} = -29.8172889607005
x4=−89.7498945058111x_{4} = -89.7498945058111
x5=32.9867228626928x_{5} = 32.9867228626928
x6=−41.793845424846x_{6} = -41.793845424846
x7=−98.9721470611453x_{7} = -98.9721470611453
x8=−27.6298211145552x_{8} = -27.6298211145552
x9=73.1875363321556x_{9} = 73.1875363321556
x10=10.7814158709709x_{10} = 10.7814158709709
x11=−25.8073176165412x_{11} = -25.8073176165412
x12=46.4234053076958x_{12} = 46.4234053076958
x13=101.526181334807x_{13} = 101.526181334807
x14=30.079539295572x_{14} = 30.079539295572
x15=−55.8815094433593x_{15} = -55.8815094433593
x16=82.2235209081029x_{16} = 82.2235209081029
x17=45.535163899664x_{17} = 45.535163899664
x18=−11.7571287633483x_{18} = -11.7571287633483
x19=−34.139872209512x_{19} = -34.139872209512
x20=18.2485292908913x_{20} = 18.2485292908913
x21=−48.9915991506973x_{21} = -48.9915991506973
x22=92.6769832808989x_{22} = 92.6769832808989
x23=−5.87856438167413x_{23} = -5.87856438167413
x24=−7.72594721818665x_{24} = -7.72594721818665
x25=−64.2743676707175x_{25} = -64.2743676707175
x26=76.9690200129499x_{26} = 76.9690200129499
x27=22.137941502317x_{27} = 22.137941502317
x28=−91.9628589348098x_{28} = -91.9628589348098
x29=77.5840932426103x_{29} = 77.5840932426103
x30=36.1511070908396x_{30} = 36.1511070908396
x31=58.1408092071534x_{31} = 58.1408092071534
x32=−3.96332729760601x_{32} = -3.96332729760601
x33=−19.8166364880301x_{33} = -19.8166364880301
x34=52.5794782701295x_{34} = 52.5794782701295
x35=−65.6765309176633x_{35} = -65.6765309176633
x36=98.1273737713015x_{36} = 98.1273737713015
x37=39.1547853391105x_{37} = 39.1547853391105
x38=−14.0684162995043x_{38} = -14.0684162995043
x39=42.2052488985128x_{39} = 42.2052488985128
x40=95.8109270062104x_{40} = 95.8109270062104
x41=−89.5396250380866x_{41} = -89.5396250380866
x42=−59.9236214113694x_{42} = -59.9236214113694
x43=−55.1173302693566x_{43} = -55.1173302693566
x44=−39.751994978311x_{44} = -39.751994978311
x45=−1.77245385090552x_{45} = -1.77245385090552
x46=−73.9349120324508x_{46} = -73.9349120324508
x47=3.96332729760601x_{47} = 3.96332729760601
x48=−22.0668724858422x_{48} = -22.0668724858422
x49=−31.2072703486357x_{49} = -31.2072703486357
x50=−58.0055663880172x_{50} = -58.0055663880172
x51=16.244807875181x_{51} = 16.244807875181
x52=52.2498231190263x_{52} = 52.2498231190263
x53=−83.8503688646267x_{53} = -83.8503688646267
x54=89.5571663498502x_{54} = 89.5571663498502
x55=28.2482660354898x_{55} = 28.2482660354898
x56=−15.7539144225679x_{56} = -15.7539144225679
x57=8.1224039375905x_{57} = 8.1224039375905
x58=−9.86860538583257x_{58} = -9.86860538583257
x59=−51.8575289757704x_{59} = -51.8575289757704
x60=83.6815990815881x_{60} = 83.6815990815881
x61=−17.9009064202391x_{61} = -17.9009064202391
x62=−43.8480866628973x_{62} = -43.8480866628973
x63=−76.8926353694292x_{63} = -76.8926353694292
x64=66.2006174575265x_{64} = 66.2006174575265
x65=23.7799637856361x_{65} = 23.7799637856361
x66=−98.9562746936211x_{66} = -98.9562746936211
x67=86.2331131935235x_{67} = 86.2331131935235
x68=70.6984717788253x_{68} = 70.6984717788253
x69=20.209083229248x_{69} = 20.209083229248
x70=0x_{70} = 0
x71=−70.6540213049065x_{71} = -70.6540213049065
x72=64.2499240996983x_{72} = 64.2499240996983
x73=−84.447707628146x_{73} = -84.447707628146
x74=−33.862683274665x_{74} = -33.862683274665
x75=54.9778714378214x_{75} = 54.9778714378214
x76=46.3217851815086x_{76} = 46.3217851815086
x77=−95.8185759344887x_{77} = -95.8185759344887
x78=−23.5619449019235x_{78} = -23.5619449019235
x79=−23.5142575266965x_{79} = -23.5142575266965
x80=61.2971843863435x_{80} = 61.2971843863435
x81=94.1071181711013x_{81} = 94.1071181711013
x82=−69.8490758065198x_{82} = -69.8490758065198
x83=39.2349385147855x_{83} = 39.2349385147855
x84=−86.1602195936888x_{84} = -86.1602195936888
x85=−61.261056745001x_{85} = -61.261056745001
x86=6.13996024767893x_{86} = 6.13996024767893
x87=−45.8103033454045x_{87} = -45.8103033454045
x88=78.9289441970977x_{88} = 78.9289441970977
x89=59.8449298194288x_{89} = 59.8449298194288
x90=10.6347231054331x_{90} = 10.6347231054331
x91=−23.8459277508708x_{91} = -23.8459277508708
x92=73.9986215763984x_{92} = 73.9986215763984
x93=−391.210720344267x_{93} = -391.210720344267
x94=66.6263492885688x_{94} = 66.6263492885688
x95=−92.6774746899941x_{95} = -92.6774746899941
x96=−67.678963415037x_{96} = -67.678963415037
x97=−77.5233303355659x_{97} = -77.5233303355659
x98=−36.3677124268396x_{98} = -36.3677124268396
x99=80.0945204032733x_{99} = 80.0945204032733
x100=61.2715531143107x_{100} = 61.2715531143107
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)*sin(x^2).
sin⁡(02)cos⁡(0)\sin{\left(0^{2} \right)} \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
2xcos⁡(x)cos⁡(x2)−sin⁡(x)sin⁡(x2)=02 x \cos{\left(x \right)} \cos{\left(x^{2} \right)} - \sin{\left(x \right)} \sin{\left(x^{2} \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=37.536735170322x_{1} = 37.536735170322
x2=−90.2995543164443x_{2} = -90.2995543164443
x3=26.7041238409344x_{3} = 26.7041238409344
x4=96.0811603317475x_{4} = 96.0811603317475
x5=2.23412500791198x_{5} = 2.23412500791198
x6=−1.67484432484861x_{6} = -1.67484432484861
x7=−33.7001911481362x_{7} = -33.7001911481362
x8=34.2088961514732x_{8} = 34.2088961514732
x9=−81.8885110144078x_{9} = -81.8885110144078
x10=−14.0032317322368x_{10} = -14.0032317322368
x11=−36.1766711135295x_{11} = -36.1766711135295
x12=−42.4203679035566x_{12} = -42.4203679035566
x13=7.7808229418531x_{13} = 7.7808229418531
x14=−59.6740765195264x_{14} = -59.6740765195264
x15=−44.0803123955744x_{15} = -44.0803123955744
x16=22.3144555829732x_{16} = 22.3144555829732
x17=78.1389021841115x_{17} = 78.1389021841115
x18=−17.7702721697402x_{18} = -17.7702721697402
x19=10.2562149360732x_{19} = 10.2562149360732
x20=−47.9381265468237x_{20} = -47.9381265468237
x21=−92.8385290764838x_{21} = -92.8385290764838
x22=94.8966350594679x_{22} = 94.8966350594679
x23=0x_{23} = 0
x24=−62.0232911735757x_{24} = -62.0232911735757
x25=26.259086539065x_{25} = 26.259086539065
x26=67.5251887322074x_{26} = 67.5251887322074
x27=−54.2410486649869x_{27} = -54.2410486649869
x28=−62.8784063418455x_{28} = -62.8784063418455
x29=−95.8526961740184x_{29} = -95.8526961740184
x30=−71.8554832810555x_{30} = -71.8554832810555
x31=−7.7808229418531x_{31} = -7.7808229418531
x32=−97.7343881376139x_{32} = -97.7343881376139
x33=−85.8039257747406x_{33} = -85.8039257747406
x34=−75.8125376133442x_{34} = -75.8125376133442
x35=92.634412032881x_{35} = 92.634412032881
x36=−67.5251887322074x_{36} = -67.5251887322074
x37=23.6214725471253x_{37} = 23.6214725471253
x38=−8.22787376837475x_{38} = -8.22787376837475
x39=99.0596546447822x_{39} = 99.0596546447822
x40=26.7424722578364x_{40} = 26.7424722578364
x41=−31.8794194517317x_{41} = -31.8794194517317
x42=51.8487347950227x_{42} = 51.8487347950227
x43=61.1809301963892x_{43} = 61.1809301963892
x44=4.13465262627828x_{44} = 4.13465262627828
x45=−5.7478922734498x_{45} = -5.7478922734498
x46=−83.972087632902x_{46} = -83.972087632902
x47=−53.7465455610153x_{47} = -53.7465455610153
x48=−3.74766067133477x_{48} = -3.74766067133477
x49=84.2894731854299x_{49} = 84.2894731854299
x50=51.8088129558038x_{50} = 51.8088129558038
x51=4.70091565676332x_{51} = 4.70091565676332
x52=54.9762522924857x_{52} = 54.9762522924857
x53=29.829741482418x_{53} = 29.829741482418
x54=6.26667579623329x_{54} = 6.26667579623329
x55=−57.6114316103265x_{55} = -57.6114316103265
x56=−73.7952790938783x_{56} = -73.7952790938783
x57=−19.9339927192786x_{57} = -19.9339927192786
x58=39.3763165001392x_{58} = 39.3763165001392
x59=−71.0200484194458x_{59} = -71.0200484194458
x60=15.9025787613332x_{60} = 15.9025787613332
x61=86.4081996571392x_{61} = 86.4081996571392
x62=−65.8556721673776x_{62} = -65.8556721673776
x63=60.2503535867024x_{63} = 60.2503535867024
x64=73.8280180700468x_{64} = 73.8280180700468
x65=−79.8291866176748x_{65} = -79.8291866176748
x66=−26.4373808099425x_{66} = -26.4373808099425
x67=−42.0743813758713x_{67} = -42.0743813758713
x68=90.3169469354969x_{68} = 90.3169469354969
x69=56.175913886337x_{69} = 56.175913886337
x70=82.461938457206x_{70} = 82.461938457206
x71=86.7145856729587x_{71} = 86.7145856729587
x72=−93.881522316429x_{72} = -93.881522316429
x73=47.7411566321408x_{73} = 47.7411566321408
x74=46.032869960288x_{74} = 46.032869960288
x75=36.1408978109486x_{75} = 36.1408978109486
x76=−17.2772507335565x_{76} = -17.2772507335565
x77=66.0699800161888x_{77} = 66.0699800161888
x78=−51.7503243924615x_{78} = -51.7503243924615
x79=62.2002992999418x_{79} = 62.2002992999418
x80=98.967318895804x_{80} = 98.967318895804
x81=−55.8393982203108x_{81} = -55.8393982203108
x82=−29.3120570723519x_{82} = -29.3120570723519
x83=−98.8528049848859x_{83} = -98.8528049848859
x84=20.4309423892029x_{84} = 20.4309423892029
x85=−45.5148417861163x_{85} = -45.5148417861163
x86=82.7850976847909x_{86} = 82.7850976847909
x87=−77.8367964156153x_{87} = -77.8367964156153
x88=14.2458403046005x_{88} = 14.2458403046005
x89=18.0328686012482x_{89} = 18.0328686012482
x90=−82.1183644934327x_{90} = -82.1183644934327
x91=−23.749242427506x_{91} = -23.749242427506
x92=−67.6216177692932x_{92} = -67.6216177692932
x93=−16.0009491904737x_{93} = -16.0009491904737
x94=42.1860239023499x_{94} = 42.1860239023499
x95=−36.0818579563209x_{95} = -36.0818579563209
x96=64.3994668189113x_{96} = 64.3994668189113
x97=−10.957767460846x_{97} = -10.957767460846
x98=−21.7443208246461x_{98} = -21.7443208246461
x99=76.4315416810569x_{99} = 76.4315416810569
Signos de extremos en los puntos:
(37.536735170321954, 0.986843498791729)

(-90.29955431644433, 0.691921908953395)

(26.704123840934372, -1.8349056647797e-5)

(96.08116033174753, -0.259528591129436)

(2.234125007911981, 0.591945725863939)

(-1.674844324848613, -0.0342921123704619)

(-33.700191148136184, 0.654363939152423)

(34.20889615147322, -0.93983071729092)

(-81.8885110144078, 0.978630114019052)

(-14.003231732236845, 0.129079844864294)

(-36.17667111352951, 0.046478368154231)

(-42.42036790355657, 0.00533064495466314)

(7.780822941853101, -0.0549592504575931)

(-59.6740765195264, 0.999869034375718)

(-44.080312395574445, 0.995199731182475)

(22.314455582973224, -0.948163233336424)

(78.13890218411152, 0.920701233646281)

(-17.770272169740206, 0.471309393582847)

(10.256214936073231, 0.672853864692745)

(-47.938126546823675, 0.686381734150551)

(-92.83852907648381, -0.160756304643403)

(94.89663505946787, 0.796769580838193)

(0, 0)

(-62.02329117357569, 0.690514702163622)

(26.25908653906497, -0.42961903305635)

(67.52518873220743, 0.0177585582888914)

(-54.24104866498691, -0.671903550807613)

(-62.87840634184554, 0.998916523665929)

(-95.8526961740184, -0.0337221111406507)

(-71.85548328105554, 0.92060942237565)

(-7.780822941853101, -0.0549592504575931)

(-97.73438813761395, -0.941068492535655)

(-85.8039257747406, 0.556233746167078)

(-75.81253761334425, -0.915388872550898)

(92.63441203288097, 0.0422207914789287)

(-67.52518873220743, 0.0177585582888914)

(23.62147254712529, -0.0560615995086132)

(-8.22787376837475, 0.360937712244325)

(99.05965464478224, -0.0991952820278843)

(26.74247225783638, 0.0350921057346341)

(-31.879419451731668, -0.894468878964384)

(51.84873479502273, 0.00984917104535034)

(61.180930196389205, 0.0796294820628317)

(4.134652626278284, 0.5369693932868)

(-5.747892273449797, 0.85897692575953)

(-83.97208763290197, -0.659280989408808)

(-53.74654556101527, 0.942926043018534)

(-3.7476606713347747, -0.818402772365498)

(84.28947318542987, 0.861012663162526)

(51.808812955803766, 0.0259101624261079)

(4.700915656763321, 0.00123051841008508)

(54.976252292485654, -0.000283792846225007)

(29.829741482418022, 0.0104073009335254)

(6.266675796233288, 0.999862853512404)

(-57.611431610326534, 0.486400074331572)

(-73.79527909387828, 0.0314522513610657)

(-19.933992719278617, 0.466885578466679)

(39.37631650013918, 0.10546498949545)

(-71.02004841944581, 0.327959090743256)

(15.902578761333166, -0.981103260528867)

(86.40819965713925, 0.0133630181218172)

(-65.85567216737758, -0.993072306512991)

(60.25035358670237, 0.847194146133567)

(73.82801807004678, 5.1328095717406e-5)

(-79.82918661767485, -0.27766072270618)

(-26.437380809942546, 0.262394827342632)

(-42.074381375871305, 0.330580102335346)

(90.31694693549686, -0.704374006726898)

(56.175913886337, 0.931322325891384)

(82.46193845720597, 0.7105282681268)

(86.71458567295866, -0.315266706524861)

(-93.88152231642897, -0.933672285597302)

(47.741156632140836, 0.815440953086963)

(46.032869960288, -0.461480368412829)

(36.14089781094858, -0.00846572461553774)

(-17.27725073355649, 7.85622449909438e-5)

(66.0699800161888, 0.995343915349401)

(-51.75032439246152, 0.0853139441750081)

(62.20029929994178, -0.80709718360807)

(98.96731889580397, -0.00583967022909107)

(-55.839398220310784, 0.758815401718861)

(-29.312057072351926, 0.507970255345382)

(-98.85280498488589, -0.10703965101645)

(20.430942389202887, -0.00420586068706861)

(-45.514841786116335, -0.0367579709104531)

(82.78509768479086, -0.450273366645496)

(-77.83679641561532, -0.762881909929572)

(14.245840304600469, -0.103248603871224)

(18.032868601248204, -0.684341420447224)

(-82.11836449343274, 0.906040577000121)

(-23.749242427506, -0.185065957824233)

(-67.62161776929321, -0.0769493800481582)

(-16.00094919047374, 0.957343240124375)

(42.18602390234994, -0.223273371835521)

(-36.081857956320945, -0.0445058898446669)

(64.39946681891129, 0.00120710383472745)

(-10.95776746084597, -0.0241222477221928)

(-21.744320824646053, -0.969676097221814)

(76.4315416810569, -0.511940665927364)


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=26.7041238409344x_{1} = 26.7041238409344
x2=96.0811603317475x_{2} = 96.0811603317475
x3=−1.67484432484861x_{3} = -1.67484432484861
x4=34.2088961514732x_{4} = 34.2088961514732
x5=7.7808229418531x_{5} = 7.7808229418531
x6=22.3144555829732x_{6} = 22.3144555829732
x7=−92.8385290764838x_{7} = -92.8385290764838
x8=0x_{8} = 0
x9=26.259086539065x_{9} = 26.259086539065
x10=−54.2410486649869x_{10} = -54.2410486649869
x11=−95.8526961740184x_{11} = -95.8526961740184
x12=−7.7808229418531x_{12} = -7.7808229418531
x13=−97.7343881376139x_{13} = -97.7343881376139
x14=−75.8125376133442x_{14} = -75.8125376133442
x15=23.6214725471253x_{15} = 23.6214725471253
x16=99.0596546447822x_{16} = 99.0596546447822
x17=−31.8794194517317x_{17} = -31.8794194517317
x18=−83.972087632902x_{18} = -83.972087632902
x19=−3.74766067133477x_{19} = -3.74766067133477
x20=54.9762522924857x_{20} = 54.9762522924857
x21=15.9025787613332x_{21} = 15.9025787613332
x22=−65.8556721673776x_{22} = -65.8556721673776
x23=−79.8291866176748x_{23} = -79.8291866176748
x24=90.3169469354969x_{24} = 90.3169469354969
x25=86.7145856729587x_{25} = 86.7145856729587
x26=−93.881522316429x_{26} = -93.881522316429
x27=46.032869960288x_{27} = 46.032869960288
x28=36.1408978109486x_{28} = 36.1408978109486
x29=62.2002992999418x_{29} = 62.2002992999418
x30=98.967318895804x_{30} = 98.967318895804
x31=−98.8528049848859x_{31} = -98.8528049848859
x32=20.4309423892029x_{32} = 20.4309423892029
x33=−45.5148417861163x_{33} = -45.5148417861163
x34=82.7850976847909x_{34} = 82.7850976847909
x35=−77.8367964156153x_{35} = -77.8367964156153
x36=14.2458403046005x_{36} = 14.2458403046005
x37=18.0328686012482x_{37} = 18.0328686012482
x38=−23.749242427506x_{38} = -23.749242427506
x39=−67.6216177692932x_{39} = -67.6216177692932
x40=42.1860239023499x_{40} = 42.1860239023499
x41=−36.0818579563209x_{41} = -36.0818579563209
x42=−10.957767460846x_{42} = -10.957767460846
x43=−21.7443208246461x_{43} = -21.7443208246461
x44=76.4315416810569x_{44} = 76.4315416810569
Puntos máximos de la función:
x44=37.536735170322x_{44} = 37.536735170322
x44=−90.2995543164443x_{44} = -90.2995543164443
x44=2.23412500791198x_{44} = 2.23412500791198
x44=−33.7001911481362x_{44} = -33.7001911481362
x44=−81.8885110144078x_{44} = -81.8885110144078
x44=−14.0032317322368x_{44} = -14.0032317322368
x44=−36.1766711135295x_{44} = -36.1766711135295
x44=−42.4203679035566x_{44} = -42.4203679035566
x44=−59.6740765195264x_{44} = -59.6740765195264
x44=−44.0803123955744x_{44} = -44.0803123955744
x44=78.1389021841115x_{44} = 78.1389021841115
x44=−17.7702721697402x_{44} = -17.7702721697402
x44=10.2562149360732x_{44} = 10.2562149360732
x44=−47.9381265468237x_{44} = -47.9381265468237
x44=94.8966350594679x_{44} = 94.8966350594679
x44=−62.0232911735757x_{44} = -62.0232911735757
x44=67.5251887322074x_{44} = 67.5251887322074
x44=−62.8784063418455x_{44} = -62.8784063418455
x44=−71.8554832810555x_{44} = -71.8554832810555
x44=−85.8039257747406x_{44} = -85.8039257747406
x44=92.634412032881x_{44} = 92.634412032881
x44=−67.5251887322074x_{44} = -67.5251887322074
x44=−8.22787376837475x_{44} = -8.22787376837475
x44=26.7424722578364x_{44} = 26.7424722578364
x44=51.8487347950227x_{44} = 51.8487347950227
x44=61.1809301963892x_{44} = 61.1809301963892
x44=4.13465262627828x_{44} = 4.13465262627828
x44=−5.7478922734498x_{44} = -5.7478922734498
x44=−53.7465455610153x_{44} = -53.7465455610153
x44=84.2894731854299x_{44} = 84.2894731854299
x44=51.8088129558038x_{44} = 51.8088129558038
x44=4.70091565676332x_{44} = 4.70091565676332
x44=29.829741482418x_{44} = 29.829741482418
x44=6.26667579623329x_{44} = 6.26667579623329
x44=−57.6114316103265x_{44} = -57.6114316103265
x44=−73.7952790938783x_{44} = -73.7952790938783
x44=−19.9339927192786x_{44} = -19.9339927192786
x44=39.3763165001392x_{44} = 39.3763165001392
x44=−71.0200484194458x_{44} = -71.0200484194458
x44=86.4081996571392x_{44} = 86.4081996571392
x44=60.2503535867024x_{44} = 60.2503535867024
x44=73.8280180700468x_{44} = 73.8280180700468
x44=−26.4373808099425x_{44} = -26.4373808099425
x44=−42.0743813758713x_{44} = -42.0743813758713
x44=56.175913886337x_{44} = 56.175913886337
x44=82.461938457206x_{44} = 82.461938457206
x44=47.7411566321408x_{44} = 47.7411566321408
x44=−17.2772507335565x_{44} = -17.2772507335565
x44=66.0699800161888x_{44} = 66.0699800161888
x44=−51.7503243924615x_{44} = -51.7503243924615
x44=−55.8393982203108x_{44} = -55.8393982203108
x44=−29.3120570723519x_{44} = -29.3120570723519
x44=−82.1183644934327x_{44} = -82.1183644934327
x44=−16.0009491904737x_{44} = -16.0009491904737
x44=64.3994668189113x_{44} = 64.3994668189113
Decrece en los intervalos
[99.0596546447822,∞)\left[99.0596546447822, \infty\right)
Crece en los intervalos
(−∞,−98.8528049848859]\left(-\infty, -98.8528049848859\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
−(4xsin⁡(x)cos⁡(x2)+2(2x2sin⁡(x2)−cos⁡(x2))cos⁡(x)+sin⁡(x2)cos⁡(x))=0- (4 x \sin{\left(x \right)} \cos{\left(x^{2} \right)} + 2 \left(2 x^{2} \sin{\left(x^{2} \right)} - \cos{\left(x^{2} \right)}\right) \cos{\left(x \right)} + \sin{\left(x^{2} \right)} \cos{\left(x \right)}) = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=48.2805848937637x_{1} = 48.2805848937637
x2=−56.3295010777896x_{2} = -56.3295010777896
x3=−67.4453697896257x_{3} = -67.4453697896257
x4=−55.9097320304548x_{4} = -55.9097320304548
x5=58.2498955757414x_{5} = 58.2498955757414
x6=−4.58027663348271x_{6} = -4.58027663348271
x7=33.3966259588525x_{7} = 33.3966259588525
x8=−64.3896590031133x_{8} = -64.3896590031133
x9=73.9357493984326x_{9} = 73.9357493984326
x10=80.0152237095484x_{10} = 80.0152237095484
x11=22.1378138965437x_{11} = 22.1378138965437
x12=−36.1608490524992x_{12} = -36.1608490524992
x13=−14.1284681644683x_{13} = -14.1284681644683
x14=−80.1063705141306x_{14} = -80.1063705141306
x15=−26.8843383894141x_{15} = -26.8843383894141
x16=41.2641804762594x_{16} = 41.2641804762594
x17=−86.3897534975876x_{17} = -86.3897534975876
x18=14.1284681644683x_{18} = 14.1284681644683
x19=22.2085820650513x_{19} = 22.2085820650513
x20=−49.2477675682454x_{20} = -49.2477675682454
x21=52.2502414206308x_{21} = 52.2502414206308
x22=71.8882840281412x_{22} = 71.8882840281412
x23=16.2437426289812x_{23} = 16.2437426289812
x24=−45.5776476276196x_{24} = -45.5776476276196
x25=−3.9355950473831x_{25} = -3.9355950473831
x26=−92.6831483360037x_{26} = -92.6831483360037
x27=−61.4005439147183x_{27} = -61.4005439147183
x28=70.6868533274074x_{28} = 70.6868533274074
x29=−98.8446570744929x_{29} = -98.8446570744929
x30=39.2597750546882x_{30} = 39.2597750546882
x31=−79.9370271941218x_{31} = -79.9370271941218
x32=98.0953090618419x_{32} = 98.0953090618419
x33=55.231841014983x_{33} = 55.231841014983
x34=−5.88578341541677x_{34} = -5.88578341541677
x35=−29.7583770522675x_{35} = -29.7583770522675
x36=−23.5990216021204x_{36} = -23.5990216021204
x37=30.0818240715464x_{37} = 30.0818240715464
x38=−39.7920425845646x_{38} = -39.7920425845646
x39=9.70686864434661x_{39} = 9.70686864434661
x40=−20.4620630674858x_{40} = -20.4620630674858
x41=−32.9911583537395x_{41} = -32.9911583537395
x42=11.4938611625289x_{42} = 11.4938611625289
x43=−65.7004770355015x_{43} = -65.7004770355015
x44=18.2495961100612x_{44} = 18.2495961100612
x45=64.2491448495299x_{45} = 64.2491448495299
x46=82.1661504352104x_{46} = 82.1661504352104
x47=32.8702594826737x_{47} = 32.8702594826737
x48=94.1238156012632x_{48} = 94.1238156012632
x49=86.2327005279146x_{49} = 86.2327005279146
x50=1.99905455339924x_{50} = 1.99905455339924
x51=−89.7501791311078x_{51} = -89.7501791311078
x52=−73.8355766068338x_{52} = -73.8355766068338
x53=−42.4695131889888x_{53} = -42.4695131889888
x54=−33.6771630371539x_{54} = -33.6771630371539
x55=102.144287081134x_{55} = 102.144287081134
x56=45.9136863650839x_{56} = 45.9136863650839
x57=0.545923613389695x_{57} = 0.545923613389695
x58=−69.8489841056869x_{58} = -69.8489841056869
x59=61.1675115362466x_{59} = 61.1675115362466
x60=67.5489233930643x_{60} = 67.5489233930643
x61=−51.7344202084962x_{61} = -51.7344202084962
x62=95.8189413791111x_{62} = 95.8189413791111
x63=−87.7678045925274x_{63} = -87.7678045925274
x64=20.2036433860741x_{64} = 20.2036433860741
x65=−11.6279295173249x_{65} = -11.6279295173249
x66=−22.0668179331993x_{66} = -22.0668179331993
x67=42.382815401685x_{67} = 42.382815401685
x68=−1.99905455339924x_{68} = -1.99905455339924
x69=76.9657183985404x_{69} = 76.9657183985404
x70=−14.3038133585414x_{70} = -14.3038133585414
x71=20.7494444613081x_{71} = 20.7494444613081
x72=4.58027663348271x_{72} = 4.58027663348271
x73=39.3208178930307x_{73} = 39.3208178930307
x74=−15.7538858101788x_{74} = -15.7538858101788
x75=−41.3781812962616x_{75} = -41.3781812962616
x76=−41.7558748666802x_{76} = -41.7558748666802
x77=−51.8403670527523x_{77} = -51.8403670527523
x78=−59.923589483352x_{78} = -59.923589483352
x79=−45.7770481619163x_{79} = -45.7770481619163
x80=6.14289001440679x_{80} = 6.14289001440679
x81=66.0343077125988x_{81} = 66.0343077125988
x82=−95.7925411076465x_{82} = -95.7925411076465
x83=89.5323414843585x_{83} = 89.5323414843585
x84=−17.9031089433338x_{84} = -17.9031089433338
x85=−98.9076814595886x_{85} = -98.9076814595886
x86=36.1608490524992x_{86} = 36.1608490524992
x87=8.32773146455807x_{87} = 8.32773146455807
x88=−77.3815559387275x_{88} = -77.3815559387275
x89=28.2482934381589x_{89} = 28.2482934381589
x90=80.1550411637371x_{90} = 80.1550411637371
x91=56.0219742475237x_{91} = 56.0219742475237
x92=45.5273998998447x_{92} = 45.5273998998447
x93=−83.2271846267013x_{93} = -83.2271846267013
x94=−51.8634746607097x_{94} = -51.8634746607097
x95=−58.1966966713285x_{95} = -58.1966966713285
x96=−9.86644425424611x_{96} = -9.86644425424611
x97=−43.812296096957x_{97} = -43.812296096957
x98=−19.8148333702786x_{98} = -19.8148333702786
x99=83.3066329713405x_{99} = 83.3066329713405

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
[95.8189413791111,∞)\left[95.8189413791111, \infty\right)
Convexa en los intervalos
(−∞,−92.6831483360037]\left(-\infty, -92.6831483360037\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(sin⁡(x2)cos⁡(x))=⟨−1,1⟩\lim_{x \to -\infty}\left(\sin{\left(x^{2} \right)} \cos{\left(x \right)}\right) = \left\langle -1, 1\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=⟨−1,1⟩y = \left\langle -1, 1\right\rangle
lim⁡x→∞(sin⁡(x2)cos⁡(x))=⟨−1,1⟩\lim_{x \to \infty}\left(\sin{\left(x^{2} \right)} \cos{\left(x \right)}\right) = \left\langle -1, 1\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=⟨−1,1⟩y = \left\langle -1, 1\right\rangle
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función cos(x)*sin(x^2), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(sin⁡(x2)cos⁡(x)x)=0\lim_{x \to -\infty}\left(\frac{\sin{\left(x^{2} \right)} \cos{\left(x \right)}}{x}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
lim⁡x→∞(sin⁡(x2)cos⁡(x)x)=0\lim_{x \to \infty}\left(\frac{\sin{\left(x^{2} \right)} \cos{\left(x \right)}}{x}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la izquierda
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:
sin⁡(x2)cos⁡(x)=sin⁡(x2)cos⁡(x)\sin{\left(x^{2} \right)} \cos{\left(x \right)} = \sin{\left(x^{2} \right)} \cos{\left(x \right)}
- Sí
sin⁡(x2)cos⁡(x)=−sin⁡(x2)cos⁡(x)\sin{\left(x^{2} \right)} \cos{\left(x \right)} = - \sin{\left(x^{2} \right)} \cos{\left(x \right)}
- No
es decir, función
es
par
    © Sr Examen – Калькулятор