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Trazado el gráfico de la función/ asin(exp(x*(9-x)))

Gráfico de la función y = asin(exp(x*(9-x)))

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
           / x*(9 - x)\
f(x) = asin\e         /
f(x)=asin⁡(ex(9−x))f{\left(x \right)} = \operatorname{asin}{\left(e^{x \left(9 - x\right)} \right)} 
f = asin(exp(x*(9 - x)))
Gráfico de la función
02468-8-6-4-2-10100.01.0
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:
asin⁡(ex(9−x))=0\operatorname{asin}{\left(e^{x \left(9 - x\right)} \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=46.4927871101477x_{1} = 46.4927871101477
x2=−22.3680583913217x_{2} = -22.3680583913217
x3=−46.1940582351326x_{3} = -46.1940582351326
x4=50.471661777902x_{4} = 50.471661777902
x5=−18.4324093149855x_{5} = -18.4324093149855
x6=20.8833138742087x_{6} = 20.8833138742087
x7=92.3657608453317x_{7} = 92.3657608453317
x8=34.5898147781968x_{8} = 34.5898147781968
x9=13.4732621084787x_{9} = 13.4732621084787
x10=−82.1134301207418x_{10} = -82.1134301207418
x11=−68.1352982698132x_{11} = -68.1352982698132
x12=−36.2417304299261x_{12} = -36.2417304299261
x13=−76.121872831763x_{13} = -76.121872831763
x14=32.614014235911x_{14} = 32.614014235911
x15=−86.1084224666236x_{15} = -86.1084224666236
x16=−5.09429181392415x_{16} = -5.09429181392415
x17=84.3773564129145x_{17} = 84.3773564129145
x18=−58.1568980733071x_{18} = -58.1568980733071
x19=88.3712822912641x_{19} = 88.3712822912641
x20=66.4143973493084x_{20} = 66.4143973493084
x21=42.5183483602605x_{21} = 42.5183483602605
x22=−72.1282353963148x_{22} = -72.1282353963148
x23=78.3876999397716x_{23} = 78.3876999397716
x24=−8.76408947391167x_{24} = -8.76408947391167
x25=100.356099413318x_{25} = 100.356099413318
x26=82.3806273025147x_{26} = 82.3806273025147
x27=76.3915311772882x_{27} = 76.3915311772882
x28=54.4539119092402x_{28} = 54.4539119092402
x29=58.4387895944219x_{29} = 58.4387895944219
x30=36.5686180676964x_{30} = 36.5686180676964
x31=11.8231544638737x_{31} = 11.8231544638737
x32=−74.1249732457446x_{32} = -74.1249732457446
x33=15.2454549240202x_{33} = 15.2454549240202
x34=−24.3425313318291x_{34} = -24.3425313318291
x35=−42.2106827505513x_{35} = -42.2106827505513
x36=−38.230414534578x_{36} = -38.230414534578
x37=−16.4737377774248x_{37} = -16.4737377774248
x38=−64.1431836862125x_{38} = -64.1431836862125
x39=−3.3867675899677x_{39} = -3.3867675899677
x40=−30.2834690006405x_{40} = -30.2834690006405
x41=−100.004779409747x_{41} = -100.004779409747
x42=38.5499000651635x_{42} = 38.5499000651635
x43=−66.1391294417549x_{43} = -66.1391294417549
x44=22.8141405305574x_{44} = 22.8141405305574
x45=48.4817452077763x_{45} = 48.4817452077763
x46=−6.90062030330136x_{46} = -6.90062030330136
x47=70.4044189917327x_{47} = 70.4044189917327
x48=−92.101687963311x_{48} = -92.101687963311
x49=74.3955814928199x_{49} = 74.3955814928199
x50=−20.397666098303x_{50} = -20.397666098303
x51=−96.0049809511308x_{51} = -96.0049809511308
x52=−52.173513705802x_{52} = -52.173513705802
x53=−80.1161114046575x_{53} = -80.1161114046575
x54=−34.2542115614781x_{54} = -34.2542115614781
x55=28.674370376629x_{55} = 28.674370376629
x56=64.419885592143x_{56} = 64.419885592143
x57=26.7126525819728x_{57} = 26.7126525819728
x58=−84.1108698153193x_{58} = -84.1108698153193
x59=−12.5852795389125x_{59} = -12.5852795389125
x60=−40.2201083386147x_{60} = -40.2201083386147
x61=−62.1474810491177x_{61} = -62.1474810491177
x62=−94.0050778835613x_{62} = -94.0050778835613
x63=−54.167597982137x_{63} = -54.167597982137
x64=−14.5236989238593x_{64} = -14.5236989238593
x65=−90.1038382165438x_{65} = -90.1038382165438
x66=86.3742452120763x_{66} = 86.3742452120763
x67=68.4092522035243x_{67} = 68.4092522035243
x68=40.5332515400496x_{68} = 40.5332515400496
x69=52.4624174664717x_{69} = 52.4624174664717
x70=94.36318434669x_{70} = 94.36318434669
x71=62.4257523828971x_{71} = 62.4257523828971
x72=−44.202029743612x_{72} = -44.202029743612
x73=−32.2680470241241x_{73} = -32.2680470241241
x74=80.3840704882711x_{74} = 80.3840704882711
x75=90.3684573054859x_{75} = 90.3684573054859
x76=96.360719922026x_{76} = 96.360719922026
x77=−88.106080858361x_{77} = -88.106080858361
x78=−26.3202993740669x_{78} = -26.3202993740669
x79=−10.6630096379263x_{79} = -10.6630096379263
x80=−28.3007657206115x_{80} = -28.3007657206115
x81=98.3583605135353x_{81} = 98.3583605135353
x82=60.4320382227969x_{82} = 60.4320382227969
x83=−48.1866908952268x_{83} = -48.1866908952268
x84=56.4460601061426x_{84} = 56.4460601061426
x85=44.5049305287302x_{85} = 44.5049305287302
x86=−50.1798616494503x_{86} = -50.1798616494503
x87=30.6418982946438x_{87} = 30.6418982946438
x88=−78.1189224254189x_{88} = -78.1189224254189
x89=−98.0048656799701x_{89} = -98.0048656799701
x90=17.0871624633497x_{90} = 17.0871624633497
x91=24.7584382700839x_{91} = 24.7584382700839
x92=−60.1520440496433x_{92} = -60.1520440496433
x93=−56.1620718424086x_{93} = -56.1620718424086
x94=−70.1316722675153x_{94} = -70.1316722675153
x95=72.3998702101123x_{95} = 72.3998702101123
x96=18.9714048149387x_{96} = 18.9714048149387
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 asin(exp(x*(9 - x))).
asin⁡(e0(9−0))\operatorname{asin}{\left(e^{0 \left(9 - 0\right)} \right)}
Resultado:
f(0)=π2f{\left(0 \right)} = \frac{\pi}{2}
Punto:
(0, pi/2)
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
(9−2x)ex(9−x)1−e2x(9−x)=0\frac{\left(9 - 2 x\right) e^{x \left(9 - x\right)}}{\sqrt{1 - e^{2 x \left(9 - x\right)}}} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=66.4144188276356x_{1} = 66.4144188276356
x2=17.0899263689562x_{2} = 17.0899263689562
x3=−32.268146617465x_{3} = -32.268146617465
x4=30.642187727879x_{4} = 30.642187727879
x5=−50.1798917899715x_{5} = -50.1798917899715
x6=20.884523551043x_{6} = 20.884523551043
x7=−34.2542965417263x_{7} = -34.2542965417263
x8=−62.147497673365x_{8} = -62.147497673365
x9=28.6747374826298x_{9} = 28.6747374826298
x10=−12.5863055170952x_{10} = -12.5863055170952
x11=64.4199092923593x_{11} = 64.4199092923593
x12=−60.1520622640927x_{12} = -60.1520622640927
x13=−5.1008195104702x_{13} = -5.1008195104702
x14=98.3583667685722x_{14} = 98.3583667685722
x15=−70.1316841006271x_{15} = -70.1316841006271
x16=−52.1735407689525x_{16} = -52.1735407689525
x17=22.8149982347286x_{17} = 22.8149982347286
x18=100.356105482242x_{18} = 100.356105482242
x19=40.5333611543142x_{19} = 40.5333611543142
x20=84.3773664031498x_{20} = 84.3773664031498
x21=48.481805306273x_{21} = 48.481805306273
x22=−82.1134376887453x_{22} = -82.1134376887453
x23=15.2500538346575x_{23} = 15.2500538346575
x24=−26.3204690788784x_{24} = -26.3204690788784
x25=−28.3009063046151x_{25} = -28.3009063046151
x26=−14.5244356600151x_{26} = -14.5244356600151
x27=−86.1084290662763x_{27} = -86.1084290662763
x28=−58.1569180872444x_{28} = -58.1569180872444
x29=−30.283586749193x_{29} = -30.283586749193
x30=42.51844159893x_{30} = 42.51844159893
x31=11.8403540900082x_{31} = 11.8403540900082
x32=−78.1189311443725x_{32} = -78.1189311443725
x33=32.6142463819744x_{33} = 32.6142463819744
x34=−38.2304778452627x_{34} = -38.2304778452627
x35=−6.90430628314868x_{35} = -6.90430628314868
x36=−98.0048787808924x_{36} = -98.0048787808924
x37=−92.1016930096301x_{37} = -92.1016930096301
x38=−18.4328254071079x_{38} = -18.4328254071079
x39=24.7590676347421x_{39} = 24.7590676347421
x40=74.3955964118507x_{40} = 74.3955964118507
x41=94.3631913509946x_{41} = 94.3631913509946
x42=−3.39969072860318x_{42} = -3.39969072860318
x43=−56.162093900683x_{43} = -56.162093900683
x44=44.5050104922868x_{44} = 44.5050104922868
x45=4.5x_{45} = 4.5
x46=−88.1060868899962x_{46} = -88.1060868899962
x47=−76.121882215662x_{47} = -76.121882215662
x48=88.3712909199937x_{48} = 88.3712909199937
x49=−94.0050769416168x_{49} = -94.0050769416168
x50=36.5687739425934x_{50} = 36.5687739425934
x51=56.4460965208043x_{51} = 56.4460965208043
x52=68.4092717290461x_{52} = 68.4092717290461
x53=92.3657683481375x_{53} = 92.3657683481375
x54=58.4388221101575x_{54} = 58.4388221101575
x55=−48.1867245973796x_{55} = -48.1867245973796
x56=−8.76635569071842x_{56} = -8.76635569071842
x57=38.5500301132873x_{57} = 38.5500301132873
x58=−66.1391434001417x_{58} = -66.1391434001417
x59=34.5900037685939x_{59} = 34.5900037685939
x60=62.4257786220294x_{60} = 62.4257786220294
x61=−80.1161195200153x_{61} = -80.1161195200153
x62=60.4320673764301x_{62} = 60.4320673764301
x63=−24.342738753825x_{63} = -24.342738753825
x64=54.453952871065x_{64} = 54.453952871065
x65=−40.2201635391922x_{65} = -40.2201635391922
x66=13.4816410675393x_{66} = 13.4816410675393
x67=−100.004779627299x_{67} = -100.004779627299
x68=−68.135311107138x_{68} = -68.135311107138
x69=−64.1431988999997x_{69} = -64.1431988999997
x70=78.387712565726x_{70} = 78.387712565726
x71=−22.3683155327555x_{71} = -22.3683155327555
x72=−44.2020724431024x_{72} = -44.2020724431024
x73=−20.3979901158107x_{73} = -20.3979901158107
x74=46.4928561998145x_{74} = 46.4928561998145
x75=72.3998864860113x_{75} = 72.3998864860113
x76=−84.1108768750305x_{76} = -84.1108768750305
x77=−36.2418035171732x_{77} = -36.2418035171732
x78=18.973184916168x_{78} = 18.973184916168
x79=−90.1038440239289x_{79} = -90.1038440239289
x80=−72.1282463272436x_{80} = -72.1282463272436
x81=−74.1249833637931x_{81} = -74.1249833637931
x82=82.3806380820164x_{82} = 82.3806380820164
x83=76.3915448860942x_{83} = 76.3915448860942
x84=96.3607265271397x_{84} = 96.3607265271397
x85=70.4044367940282x_{85} = 70.4044367940282
x86=52.4624637640073x_{86} = 52.4624637640073
x87=−46.1940960821807x_{87} = -46.1940960821807
x88=90.3684653455661x_{88} = 90.3684653455661
x89=−96.0049695080707x_{89} = -96.0049695080707
x90=−42.2107311674476x_{90} = -42.2107311674476
x91=−54.1676223726593x_{91} = -54.1676223726593
x92=86.3742544880409x_{92} = 86.3742544880409
x93=−16.4742841415853x_{93} = -16.4742841415853
x94=−10.6644965281302x_{94} = -10.6644965281302
x95=26.713127614282x_{95} = 26.713127614282
x96=50.4717143780255x_{96} = 50.4717143780255
x97=80.3840821424105x_{97} = 80.3840821424105
Signos de extremos en los puntos:
(66.4144188276356, 9.37681663285521e-1657)

(17.089926368956167, 9.03806133126165e-61)

(-32.26814661746504, 4.71223896947148e-579)

(30.64218772787897, 9.80715945530183e-289)

(-50.17989178997149, 2.00211435437063e-1290)

(20.88452355104299, 1.61055372538116e-108)

(-34.254296541726276, 3.38481565028336e-644)

(-62.14749767336496, 5.0886751935755e-1921)

(28.67473748262979, 9.66006640543522e-246)

(-12.586305517095177, 1.01329231750078e-118)

(64.41990929235934, 3.20255724329527e-1551)

(-60.15206226409275, 3.10218915133608e-1807)

(-5.100819510470203, 5.79495495211922e-32)

(98.35836676857218, 8.38859116019242e-3818)

(-70.13168410062706, 6.64847505182184e-2411)

(-52.17354076895255, 7.7314829882535e-1387)

(22.8149982347286, 1.30342758956372e-137)

(100.35610548224244, 2.11886820275147e-3982)

(40.53336115431421, 8.0381232349166e-556)

(84.37736640314976, 6.6788675151078e-2763)

(48.48180530627295, 4.9609605047794e-832)

(-82.11343768874535, 5.83552343894517e-3250)

(15.250053834657459, 4.03463749572234e-42)

(-26.3204690788784, 1.80952309565193e-404)

(-28.300906304615058, 3.4456180045941e-459)

(-14.524435660015119, 4.07971312750441e-149)

(-86.10842906627634, 1.93045923727884e-3557)

(-58.15691808724441, 6.34405795211994e-1697)

(-30.283586749192967, 2.20028289182126e-517)

(42.518441598930046, 1.15982711133724e-619)

(11.840354090008164, 2.47930487416239e-15)

(-78.11893114437248, 2.23390561815409e-2956)

(32.614246381974446, 3.33728141063949e-335)

(-38.23047784526274, 6.59005118684743e-785)

(-6.904306283148685, 2.04599180848749e-48)

(-98.00487878089243, 3.57843195272025e-4555)

(-92.10169300963013, 1.01716947075911e-4044)

(-18.432825407107853, 2.4700522537948e-220)

(24.759067634742106, 3.52416799963459e-170)

(74.39559641185075, 1.24346735088651e-2113)

(94.36319135099455, 4.96334843516895e-3499)

(-3.3996907286031814, 4.92341876096112e-19)

(-56.162093900683004, 4.35211287361712e-1590)

(44.50501049228682, 5.6130508706849e-687)

(4.5, 1.5707963267949 - 20.9431471805599*I)

(-88.10608688999616, 2.1573410938504e-3716)

(-76.12188221566203, 8.49217186552595e-2815)

(88.37129091999367, 6.25472868103262e-3047)

(-94.00507694161679, 5.32662515847277e-4206)

(36.56877394259343, 1.45645958678613e-438)

(56.4460965208043, 7.86249901188406e-1164)

(68.40927172904611, 9.20973696767685e-1766)

(92.36576834813751, 7.41784553994878e-3345)

(58.43882211015752, 1.81804377897527e-1255)

(-48.18672459737958, 1.73916917532745e-1197)

(-8.766355690718424, 2.29238557452821e-68)

(38.55003011328726, 1.86837733016379e-495)

(-66.13914340014168, 5.1687737172543e-2159)

(34.590003768593895, 3.80735228300443e-385)

(62.42577862202938, 3.66918945239814e-1449)

(-80.11611952001527, 1.97129512189772e-3101)

(60.432067376430055, 1.4101760298323e-1350)

(-24.34273875382503, 3.18661430093067e-353)

(54.45395287106497, 1.140614924026e-1075)

(-40.22016353919216, 1.7863117205155e-860)

(13.481641067539305, 5.7541494885676e-27)

(-100.00477962729933, 5.70561271050931e-4735)

(-68.13531110713797, 3.20063002963158e-2283)

(-64.14319889999966, 2.80012566617479e-2038)

(78.387712565726, 6.45275098761121e-2363)

(-22.36831553275548, 1.88150839983087e-305)

(-44.20207244310242, 4.95355146360078e-1022)

(-20.397990115810703, 3.72399666710953e-261)

(46.49285619981447, 9.11142090565432e-758)

(72.3998864860113, 3.35378854872573e-1994)

(-84.11087687503048, 5.79494394604581e-3402)

(-36.241803517173196, 8.15488776134898e-713)

(18.97318491616799, 6.62917989794848e-83)

(-90.10384402392891, 8.0871114874881e-3879)

(-72.12824632724364, 4.63284524046397e-2542)

(-74.12498336379312, 1.08296201693494e-2676)

(82.38063808201643, 4.24043619586672e-2626)

(76.39154488609422, 1.54657347942856e-2236)

(96.36072652713975, 1.11407213469372e-3656)

(70.40443679402819, 3.03440544180516e-1878)

(52.462463764007275, 5.55054900889994e-991)

(-46.1940960821807, 5.06779315671686e-1108)

(90.36846534556612, 3.71896803663157e-3194)

(-96.00496950807069, 7.54757562714969e-4379)

(-42.21073116744759, 1.62416871330881e-939)

(-54.16762237265933, 1.00153450434307e-1486)

(86.37425448804089, 3.52886746926088e-2903)

(-16.474284141585258, 5.48752188174733e-183)

(-10.664496528130183, 8.38021527898054e-92)

(26.713127614281984, 3.18830921104464e-206)

(50.47171437802554, 9.06038641512723e-910)

(80.3840821424105, 9.03146181002677e-2493)


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:
La función no tiene puntos mínimos
La función no tiene puntos máximos
Decrece en todo el eje numérico
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
((2x−9)2−2+(2x−9)2e−2x(x−9)1−e2x(9−x))e−x(x−9)1−e2x(9−x)=0\frac{\left(\left(2 x - 9\right)^{2} - 2 + \frac{\left(2 x - 9\right)^{2} e^{- 2 x \left(x - 9\right)}}{1 - e^{2 x \left(9 - x\right)}}\right) e^{- x \left(x - 9\right)}}{\sqrt{1 - e^{2 x \left(9 - x\right)}}} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−34.254381635506x_{1} = -34.254381635506
x2=−60.1520804872676x_{2} = -60.1520804872676
x3=32.6144791191814x_{3} = 32.6144791191814
x4=−84.1108839441564x_{4} = -84.1108839441564
x5=−37627010557352.2x_{5} = -37627010557352.2
x6=−54.1676467773744x_{6} = -54.1676467773744
x7=−2109.45700680773x_{7} = -2109.45700680773
x8=13.4902458822592x_{8} = 13.4902458822592
x9=48.4818654670654x_{9} = 48.4818654670654
x10=40.5334709380707x_{10} = 40.5334709380707
x11=44.5050905560828x_{11} = 44.5050905560828
x12=76.3915586002076x_{12} = 76.3915586002076
x13=−62.1475143051055x_{13} = -62.1475143051055
x14=74.395611336994x_{14} = 74.395611336994
x15=36.5689301221016x_{15} = 36.5689301221016
x16=−80.1161276367699x_{16} = -80.1161276367699
x17=−5.10750078550252x_{17} = -5.10750078550252
x18=98.3583729112059x_{18} = 98.3583729112059
x19=−58.1569381113902x_{19} = -58.1569381113902
x20=−36.2418766927414x_{20} = -36.2418766927414
x21=−28.301047151143x_{21} = -28.301047151143
x22=−3.41308381939881x_{22} = -3.41308381939881
x23=100.356110915876x_{23} = 100.356110915876
x24=84.3773763965943x_{24} = 84.3773763965943
x25=−14.5251765300086x_{25} = -14.5251765300086
x26=−42.2107796288234x_{26} = -42.2107796288234
x27=−86.1084356631547x_{27} = -86.1084356631547
x28=−72.1282572618827x_{28} = -72.1282572618827
x29=38.5501603867115x_{29} = 38.5501603867115
x30=30.6424780144044x_{30} = 30.6424780144044
x31=−50.179921950687x_{31} = -50.179921950687
x32=−82.1134452607206x_{32} = -82.1134452607206
x33=−94.0050743237927x_{33} = -94.0050743237927
x34=20.8857424273909x_{34} = 20.8857424273909
x35=−92.1016985212211x_{35} = -92.1016985212211
x36=18.9749824857761x_{36} = 18.9749824857761
x37=−22.3685733915089x_{37} = -22.3685733915089
x38=80.3840938006122x_{38} = 80.3840938006122
x39=−46.1941339587386x_{39} = -46.1941339587386
x40=−52.1735678489804x_{40} = -52.1735678489804
x41=96.360733133599x_{41} = 96.360733133599
x42=−66.1391573641318x_{42} = -66.1391573641318
x43=−74.124993485196x_{43} = -74.124993485196
x44=82.3806488651423x_{44} = 82.3806488651423
x45=−88.1060931321837x_{45} = -88.1060931321837
x46=−18.4332430971178x_{46} = -18.4332430971178
x47=11.8582892502723x_{47} = 11.8582892502723
x48=28.6751058559075x_{48} = 28.6751058559075
x49=60.4320965487307x_{49} = 60.4320965487307
x50=1.0315876058831⋅1017x_{50} = 1.0315876058831 \cdot 10^{17}
x51=−56.1621159709617x_{51} = -56.1621159709617
x52=−98.0048790136004x_{52} = -98.0048790136004
x53=−38.23054122548x_{53} = -38.23054122548
x54=62.4258048768246x_{54} = 62.4258048768246
x55=86.3742637667604x_{55} = 86.3742637667604
x56=94.3631983715641x_{56} = 94.3631983715641
x57=46.4929253680612x_{57} = 46.4929253680612
x58=−32.268246358677x_{58} = -32.268246358677
x59=−20.3983151872144x_{59} = -20.3983151872144
x60=−6.90805214265083x_{60} = -6.90805214265083
x61=17.0927264960382x_{61} = 17.0927264960382
x62=−26.3206391428518x_{62} = -26.3206391428518
x63=92.3657758562425x_{63} = 92.3657758562425
x64=70.4044546045305x_{64} = 70.4044546045305
x65=22.8158611350303x_{65} = 22.8158611350303
x66=50.4717670280435x_{66} = 50.4717670280435
x67=−64.143214120251x_{67} = -64.143214120251
x68=72.3999027689785x_{68} = 72.3999027689785
x69=−76.1218916025258x_{69} = -76.1218916025258
x70=56.4461329625053x_{70} = 56.4461329625053
x71=54.4539938657847x_{71} = 54.4539938657847
x72=34.5901931787706x_{72} = 34.5901931787706
x73=−44.2021151786712x_{73} = -44.2021151786712
x74=66.4144403171831x_{74} = 66.4144403171831
x75=52.4625101018812x_{75} = 52.4625101018812
x76=58.4388546482833x_{76} = 58.4388546482833
x77=−96.0049744081576x_{77} = -96.0049744081576
x78=68.4092912641406x_{78} = 68.4092912641406
x79=78.3877251963013x_{79} = 78.3877251963013
x80=−12.5873386663431x_{80} = -12.5873386663431
x81=15.2547368089636x_{81} = 15.2547368089636
x82=−40.2202187951075x_{82} = -40.2202187951075
x83=90.3684733862232x_{83} = 90.3684733862232
x84=−8.76864866338856x_{84} = -8.76864866338856
x85=−68.1353239493314x_{85} = -68.1353239493314
x86=30100954270.4482x_{86} = 30100954270.4482
x87=−48.1867583238569x_{87} = -48.1867583238569
x88=−24.3429466774556x_{88} = -24.3429466774556
x89=−100.004815122136x_{89} = -100.004815122136
x90=88.3712995506551x_{90} = 88.3712995506551
x91=−30.2837046931748x_{91} = -30.2837046931748
x92=64.4199330057959x_{92} = 64.4199330057959
x93=−78.1189398655109x_{93} = -78.1189398655109
x94=−90.1038498325187x_{94} = -90.1038498325187
x95=−16.4748330197422x_{95} = -16.4748330197422
x96=24.7597001055415x_{96} = 24.7597001055415
x97=−70.1316959379875x_{97} = -70.1316959379875
x98=−10.6659967073356x_{98} = -10.6659967073356
x99=26.7136045921971x_{99} = 26.7136045921971
x100=42.5185349670573x_{100} = 42.5185349670573

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:
No tiene corvaduras en todo el eje numérico
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞asin⁡(ex(9−x))=0\lim_{x \to -\infty} \operatorname{asin}{\left(e^{x \left(9 - x\right)} \right)} = 0
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=0y = 0
lim⁡x→∞asin⁡(ex(9−x))=0\lim_{x \to \infty} \operatorname{asin}{\left(e^{x \left(9 - x\right)} \right)} = 0
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=0y = 0
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función asin(exp(x*(9 - x))), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(asin⁡(ex(9−x))x)=0\lim_{x \to -\infty}\left(\frac{\operatorname{asin}{\left(e^{x \left(9 - x\right)} \right)}}{x}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
lim⁡x→∞(asin⁡(ex(9−x))x)=0\lim_{x \to \infty}\left(\frac{\operatorname{asin}{\left(e^{x \left(9 - x\right)} \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:
asin⁡(ex(9−x))=asin⁡(e−x(x+9))\operatorname{asin}{\left(e^{x \left(9 - x\right)} \right)} = \operatorname{asin}{\left(e^{- x \left(x + 9\right)} \right)}
- No
asin⁡(ex(9−x))=−asin⁡(e−x(x+9))\operatorname{asin}{\left(e^{x \left(9 - x\right)} \right)} = - \operatorname{asin}{\left(e^{- x \left(x + 9\right)} \right)}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор