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Trazado el gráfico de la función/ (-4*cos(2*x)+3*sin(2*x)-10*x*cos(2*x)-5*x*sin(2*x))*exp(2)/25

Gráfico de la función y = (-4*cos(2*x)+3*sin(2*x)-10*x*cos(2*x)-5*x*sin(2*x))*exp(2)/25

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
                                                                  2
       (-4*cos(2*x) + 3*sin(2*x) - 10*x*cos(2*x) - 5*x*sin(2*x))*e 
f(x) = ------------------------------------------------------------
                                    25
f(x)=(−5xsin⁡(2x)+(−10xcos⁡(2x)+(3sin⁡(2x)−4cos⁡(2x))))e225f{\left(x \right)} = \frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2}}{25} 
f = ((-5*x*sin(2*x) - 10*x*cos(2*x) + 3*sin(2*x) - 4*cos(2*x))*exp(2))/25
Gráfico de la función
02468-8-6-4-2-1010-5050
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:
(−5xsin⁡(2x)+(−10xcos⁡(2x)+(3sin⁡(2x)−4cos⁡(2x))))e225=0\frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2}}{25} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=−82.2325453148142x_{1} = -82.2325453148142
x2=48.1369742468376x_{2} = 48.1369742468376
x3=92.1212425868993x_{3} = 92.1212425868993
x4=71.7002750718382x_{4} = 71.7002750718382
x5=−97.9409004053142x_{5} = -97.9409004053142
x6=−63.3822620275935x_{6} = -63.3822620275935
x7=−53.9569290879675x_{7} = -53.9569290879675
x8=−96.3700706562873x_{8} = -96.3700706562873
x9=−90.0867399786036x_{9} = -90.0867399786036
x10=−49.2441826243389x_{10} = -49.2441826243389
x11=−83.8033874497159x_{11} = -83.8033874497159
x12=−77.52000774231x_{12} = -77.52000774231
x13=38.711194082931x_{13} = 38.711194082931
x14=27.7135950463327x_{14} = 27.7135950463327
x15=10.4231820678823x_{15} = 10.4231820678823
x16=13.5690713585147x_{16} = 13.5690713585147
x17=−30.392080701905x_{17} = -30.392080701905
x18=33.998096818604x_{18} = 33.998096818604
x19=35.5691499799686x_{19} = 35.5691499799686
x20=77.9836839246782x_{20} = 77.9836839246782
x21=24.5710936445514x_{21} = 24.5710936445514
x22=−25.6784664664367x_{22} = -25.6784664664367
x23=−6.80652346886145x_{23} = -6.80652346886145
x24=−5.22625597509219x_{24} = -5.22625597509219
x25=−75.9491577762104x_{25} = -75.9491577762104
x26=−69.6657336523285x_{26} = -69.6657336523285
x27=−2.01596760929877x_{27} = -2.01596760929877
x28=−11.5315060675231x_{28} = -11.5315060675231
x29=−31.9632046337359x_{29} = -31.9632046337359
x30=85.8378990745764x_{30} = 85.8378990745764
x31=−61.8113849962171x_{31} = -61.8113849962171
x32=−47.6732513637146x_{32} = -47.6732513637146
x33=57.562427329489x_{33} = 57.562427329489
x34=−68.0948707145325x_{34} = -68.0948707145325
x35=70.1294166172771x_{35} = 70.1294166172771
x36=−19.3927111661874x_{36} = -19.3927111661874
x37=−88.5159040771196x_{37} = -88.5159040771196
x38=93.692075156457x_{38} = 93.692075156457
x39=16.7133624699783x_{39} = 16.7133624699783
x40=−17.8209857998202x_{40} = -17.8209857998202
x41=84.2670595187915x_{41} = 84.2670595187915
x42=−9.95786750711371x_{42} = -9.95786750711371
x43=76.4128351491376x_{43} = 76.4128351491376
x44=2.51487634015187x_{44} = 2.51487634015187
x45=−27.2497186610371x_{45} = -27.2497186610371
x46=40.2821898543443x_{46} = 40.2821898543443
x47=−16.2490784315059x_{47} = -16.2490784315059
x48=54.4206355245892x_{48} = 54.4206355245892
x49=−55.5278310424106x_{49} = -55.5278310424106
x50=82.6962183246632x_{50} = 82.6962183246632
x51=90.5504087626561x_{51} = 90.5504087626561
x52=11.9964038547978x_{52} = 11.9964038547978
x53=22.9997506147888x_{53} = 22.9997506147888
x54=19.8568075344756x_{54} = 19.8568075344756
x55=62.2750774800987x_{55} = 62.2750774800987
x56=99.9753940683265x_{56} = 99.9753940683265
x57=0.832403564977084x_{57} = 0.832403564977084
x58=−60.2405037417412x_{58} = -60.2405037417412
x59=−39.8184345452483x_{59} = -39.8184345452483
x60=68.5585553239472x_{60} = 68.5585553239472
x61=32.4270189220146x_{61} = 32.4270189220146
x62=63.8459523224512x_{62} = 63.8459523224512
x63=4.11257088016x_{63} = 4.11257088016
x64=−71.2365936441077x_{64} = -71.2365936441077
x65=−74.3783055382886x_{65} = -74.3783055382886
x66=−38.2474297987677x_{66} = -38.2474297987677
x67=98.4045659366674x_{67} = 98.4045659366674
x68=−33.5342976831179x_{68} = -33.5342976831179
x69=18.2851637632985x_{69} = 18.2851637632985
x70=−8.38313491957301x_{70} = -8.38313491957301
x71=−91.6575745206459x_{71} = -91.6575745206459
x72=79.5545306341413x_{72} = 79.5545306341413
x73=−99.5117290970474x_{73} = -99.5117290970474
x74=−93.2284077721128x_{74} = -93.2284077721128
x75=60.7041985874648x_{75} = 60.7041985874648
x76=41.8531707240276x_{76} = 41.8531707240276
x77=46.5660389415817x_{77} = 46.5660389415817
x78=−46.1023108671164x_{78} = -46.1023108671164
x79=−85.3742278949593x_{79} = -85.3742278949593
x80=−24.1071543447115x_{80} = -24.1071543447115
x81=5.69574005599237x_{81} = 5.69574005599237
x82=−52.3860207742208x_{82} = -52.3860207742208
x83=49.7079008028105x_{83} = 49.7079008028105
x84=26.1423714491946x_{84} = 26.1423714491946
x85=55.9915342108209x_{85} = 55.9915342108209
x86=−41.3894233927615x_{86} = -41.3894233927615
x87=−3.63724136542249x_{87} = -3.63724136542249
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 ((-4*cos(2*x) + 3*sin(2*x) - 10*x*cos(2*x) - 5*x*sin(2*x))*exp(2))/25.
(((−4cos⁡(0⋅2)+3sin⁡(0⋅2))−0⋅10cos⁡(0⋅2))−0⋅5sin⁡(0⋅2))e225\frac{\left(\left(\left(- 4 \cos{\left(0 \cdot 2 \right)} + 3 \sin{\left(0 \cdot 2 \right)}\right) - 0 \cdot 10 \cos{\left(0 \cdot 2 \right)}\right) - 0 \cdot 5 \sin{\left(0 \cdot 2 \right)}\right) e^{2}}{25}
Resultado:
f(0)=−4e225f{\left(0 \right)} = - \frac{4 e^{2}}{25}
Punto:
(0, -4*exp(2)/25)
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
(20xsin⁡(2x)−10xcos⁡(2x)+3sin⁡(2x)−4cos⁡(2x))e225=0\frac{\left(20 x \sin{\left(2 x \right)} - 10 x \cos{\left(2 x \right)} + 3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right) e^{2}}{25} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=64.6352443879741x_{1} = 64.6352443879741
x2=−72.0255033591792x_{2} = -72.0255033591792
x3=−35.8978923510335x_{3} = -35.8978923510335
x4=−67.3131632574602x_{4} = -67.3131632574602
x5=−94.0164887583458x_{5} = -94.0164887583458
x6=−100.2996406125x_{6} = -100.2996406125
x7=−79.8794163763463x_{7} = -79.8794163763463
x8=−51.6054276384411x_{8} = -51.6054276384411
x9=45.7860045671659x_{9} = 45.7860045671659
x10=37.9322468707416x_{10} = 37.9322468707416
x11=52.06905917643x_{11} = 52.06905917643
x12=−23.3322825654232x_{12} = -23.3322825654232
x13=100.763283948745x_{13} = 100.763283948745
x14=−70.4547225967174x_{14} = -70.4547225967174
x15=20.6545735900731x_{15} = 20.6545735900731
x16=−57.8885070098078x_{16} = -57.8885070098078
x17=−64.1716071901995x_{17} = -64.1716071901995
x18=−1.38120160239195x_{18} = -1.38120160239195
x19=9.66167172579424x_{19} = 9.66167172579424
x20=−7.62888790549685x_{20} = -7.62888790549685
x21=−21.7616436866734x_{21} = -21.7616436866734
x22=39.5029913226638x_{22} = 39.5029913226638
x23=−26.4736167915785x_{23} = -26.4736167915785
x24=−89.3041279638035x_{24} = -89.3041279638035
x25=58.3521418348081x_{25} = 58.3521418348081
x26=86.6261976410267x_{26} = 86.6261976410267
x27=1.82726394043287x_{27} = 1.82726394043287
x28=44.2152466924093x_{28} = 44.2152466924093
x29=−78.308632669004x_{29} = -78.308632669004
x30=−45.3223777683704x_{30} = -45.3223777683704
x31=88.1969837349327x_{31} = 88.1969837349327
x32=67.7768014012035x_{32} = 67.7768014012035
x33=80.3430572566921x_{33} = 80.3430572566921
x34=−86.1625558175537x_{34} = -86.1625558175537
x35=30.0786053386116x_{35} = 30.0786053386116
x36=31.6493202274584x_{36} = 31.6493202274584
x37=14.3724218304636x_{37} = 14.3724218304636
x38=83.4846266056516x_{38} = 83.4846266056516
x39=61.4936910044344x_{39} = 61.4936910044344
x40=66.2060224730732x_{40} = 66.2060224730732
x41=50.4982924871669x_{41} = 50.4982924871669
x42=53.6398275949959x_{42} = 53.6398275949959
x43=42.6444916370061x_{43} = 42.6444916370061
x44=17.5134060900679x_{44} = 17.5134060900679
x45=−50.0346619693212x_{45} = -50.0346619693212
x46=−81.4502005716198x_{46} = -81.4502005716198
x47=−95.5872763087217x_{47} = -95.5872763087217
x48=0.325795503797285x_{48} = 0.325795503797285
x49=−59.4592803626043x_{49} = -59.4592803626043
x50=75.6307068537696x_{50} = 75.6307068537696
x51=−28.0443057693738x_{51} = -28.0443057693738
x52=−12.33866578552x_{52} = -12.33866578552
x53=−20.1910295447822x_{53} = -20.1910295447822
x54=81.9138417082726x_{54} = 81.9138417082726
x55=−37.4686296462638x_{55} = -37.4686296462638
x56=72.4891426972687x_{56} = 72.4891426972687
x57=−6.05989325317838x_{57} = -6.05989325317838
x58=−42.180868035436x_{58} = -42.180868035436
x59=6.52244633170316x_{59} = 6.52244633170316
x60=23.7958523877927x_{60} = 23.7958523877927
x61=−34.3271604895018x_{61} = -34.3271604895018
x62=96.0509192143605x_{62} = 96.0509192143605
x63=8.09183517436296x_{63} = 8.09183517436296
x64=−73.5962847878296x_{64} = -73.5962847878296
x65=−15.4794117940065x_{65} = -15.4794117940065
x66=22.2252019991699x_{66} = 22.2252019991699
x67=−43.7516214066214x_{67} = -43.7516214066214
x68=−92.4457015068628x_{68} = -92.4457015068628
x69=−56.3177349431024x_{69} = -56.3177349431024
x70=−65.742384785425x_{70} = -65.742384785425
x71=−48.46389829568x_{71} = -48.46389829568
x72=89.7677701861569x_{72} = 89.7677701861569
x73=36.3615068758865x_{73} = 36.3615068758865
x74=85.0554119241887x_{74} = 85.0554119241887
x75=28.5078993606643x_{75} = 28.5078993606643
x76=15.9428843727392x_{76} = 15.9428843727392
x77=−29.6150062107158x_{77} = -29.6150062107158
x78=−87.7333417066779x_{78} = -87.7333417066779
x79=74.0599244741303x_{79} = 74.0599244741303
x80=−122.290699217015x_{80} = -122.290699217015
x81=−13.9089903135835x_{81} = -13.9089903135835
x82=97.621707199601x_{82} = 97.621707199601
x83=94.4801315058989x_{83} = 94.4801315058989
x84=59.9229158515985x_{84} = 59.9229158515985
Signos de extremos en los puntos:
                                      2 
(64.63524438797407, 28.9948923620801*e )

                                       2 
(-72.02550335917921, 32.1210614185897*e )

                                        2 
(-35.89789235103348, -15.9640190445123*e )

                                       2 
(-67.3131632574602, -30.0136191852217*e )

                                      2 
(-94.0164887583458, 41.9557947445377*e )

                                        2 
(-100.29964061249967, 44.7657191408808*e )

                                        2 
(-79.87941637634631, -35.6334657154449*e )

                                        2 
(-51.60542763844109, -22.9888146351093*e )

                                      2 
(45.78600456716588, 20.5651288215444*e )

                                       2 
(37.93224687074159, -17.0527314711191*e )

                                       2 
(52.069059176430024, 23.3750488688439*e )

                                         2 
(-23.332282565423245, -10.3442012872768*e )

                                        2 
(100.76328394874524, -45.1519539022625*e )

                                       2 
(-70.45472259671737, -31.418580641551*e )

                                       2 
(20.654573590073127, 9.32548385202523*e )

                                         2 
(-57.888507009807775, -25.7987357898477*e )

                                       2 
(-64.17160719019948, -28.608657875224*e )

                                          2 
(-1.3812016023919491, -0.511276106334118*e )

                                      2 
(9.66167172579424, -4.40823309118173*e )

                                         2 
(-7.6288879054968515, -3.31959096286351*e )

                                        2 
(-21.761643686673448, 9.64172685620577*e )

                                      2 
(39.50299132266381, 17.7552106242279*e )

                                        2 
(-26.473616791578547, -11.749152675255*e )

                                        2 
(-89.30412796380352, -39.8483515857425*e )

                                      2 
(58.35214183480807, 26.1849701705871*e )

                                      2 
(86.62619764102669, 38.8296242503845*e )

                                        2 
(1.8272639404328703, 0.896705738789304*e )

                                      2 
(44.21524669240928, -19.862649068112*e )

                                       2 
(-78.30863266900396, 34.9309848067047*e )

                                         2 
(-45.322377768370444, -20.1788947997625*e )

                                       2 
(88.19698373493272, -39.5321052658568*e )

                                      2 
(67.77680140120351, 30.3998537143839*e )

                                     2 
(80.34305725669208, 36.019700366994*e )

                                       2 
(-86.1625558175537, -38.4433895566568*e )

                                       2 
(30.078605338611613, 13.5403393161195*e )

                                        2 
(31.649320227458396, -14.2428171470094*e )

                                       2 
(14.372421830463598, 6.51560418959179*e )

                                      2 
(83.48462660565158, 37.4246622709793*e )

                                      2 
(61.493691004434396, 27.589931172105*e )

                                       2 
(66.20602247307319, -29.6973730193808*e )

                                       2 
(50.49829248716687, -22.6725687211968*e )

                                       2 
(53.63982759499592, -24.0775290938307*e )

                                      2 
(42.64449163700615, 19.1601694407716*e )

                                     2 
(17.51340609006795, 7.9205399219896*e )

                                      2 
(-50.0346619693212, 22.2863345330862*e )

                                       2 
(-81.45020057161976, 36.3359466460064*e )

                                       2 
(-95.58727630872174, -42.658275825146*e )

                                         2 
(0.3257955037972845, -0.197579404789642*e )

                                       2 
(-59.45928036260429, 26.5012162355076*e )

                                       2 
(75.63070685376955, -33.9122576729332*e )

                                       2 
(-28.044305769373786, 12.451629347221*e )

                                       2 
(-12.33866578552004, 5.42691853666759*e )

                                         2 
(-20.191029544782236, -8.93925353165252*e )

                                       2 
(81.91384170827256, -36.7221813090182*e )

                                       2 
(-37.46862964626381, 16.6664978775403*e )

                                       2 
(72.48914269726872, -32.5072960011658*e )

                                       2 
(-6.059893253178378, 2.61719016207641*e )

                                        2 
(-42.18086803543602, -18.7739355619817*e )

                                      2 
(6.52244633170316, -3.00337610001784*e )

                                     2 
(23.795852387792745, 10.73043276069*e )

                                       2 
(-34.32716048950175, 15.2615404545068*e )

                                      2 
(96.05091921436053, 43.0445105672703*e )

                                     2 
(8.09183517436296, 3.70579456836871*e )

                                        2 
(-73.59628478782957, -32.8235422254219*e )

                                       2 
(-15.479411794006543, 6.8318436088485*e )

                                        2 
(22.225201999169858, -10.0279578147771*e )

                                       2 
(-43.75162140662138, 19.4764151139974*e )

                                        2 
(-92.44570150686276, -41.2533136772963*e )

                                      2 
(-56.3177349431024, 25.0962554017054*e )

                                       2 
(-65.74238478542499, 29.3111385106163*e )

                                         2 
(-48.463898295680046, -21.5838545203074*e )

                                     2 
(89.76777018615694, 40.234586297309*e )

                                      2 
(36.36150687588652, 16.3502525173509*e )

                                       2 
(85.05541192418873, -38.1271432517755*e )

                                      2 
(28.50789936066434, -12.837861883783*e )

                                        2 
(15.942884372739243, -7.21807073205542*e )

                                         2 
(-29.615006210715844, -13.1541065319221*e )

                                       2 
(-87.73334170667792, 39.1458705629708*e )

                                      2 
(74.05992447413026, 33.2097768235707*e )

                                       2 
(-122.2906992170149, 54.6004557407121*e )

                                         2 
(-13.908990313583539, -6.12937890360175*e )

                                       2 
(97.62170719960096, -43.7469916673266*e )

                                     2 
(94.4801315058989, -42.342029479592*e )

                                       2 
(59.92291585159847, -26.8874506459426*e )


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=−35.8978923510335x_{1} = -35.8978923510335
x2=−67.3131632574602x_{2} = -67.3131632574602
x3=−79.8794163763463x_{3} = -79.8794163763463
x4=−51.6054276384411x_{4} = -51.6054276384411
x5=37.9322468707416x_{5} = 37.9322468707416
x6=−23.3322825654232x_{6} = -23.3322825654232
x7=100.763283948745x_{7} = 100.763283948745
x8=−70.4547225967174x_{8} = -70.4547225967174
x9=−57.8885070098078x_{9} = -57.8885070098078
x10=−64.1716071901995x_{10} = -64.1716071901995
x11=−1.38120160239195x_{11} = -1.38120160239195
x12=9.66167172579424x_{12} = 9.66167172579424
x13=−7.62888790549685x_{13} = -7.62888790549685
x14=−26.4736167915785x_{14} = -26.4736167915785
x15=−89.3041279638035x_{15} = -89.3041279638035
x16=44.2152466924093x_{16} = 44.2152466924093
x17=−45.3223777683704x_{17} = -45.3223777683704
x18=88.1969837349327x_{18} = 88.1969837349327
x19=−86.1625558175537x_{19} = -86.1625558175537
x20=31.6493202274584x_{20} = 31.6493202274584
x21=66.2060224730732x_{21} = 66.2060224730732
x22=50.4982924871669x_{22} = 50.4982924871669
x23=53.6398275949959x_{23} = 53.6398275949959
x24=−95.5872763087217x_{24} = -95.5872763087217
x25=0.325795503797285x_{25} = 0.325795503797285
x26=75.6307068537696x_{26} = 75.6307068537696
x27=−20.1910295447822x_{27} = -20.1910295447822
x28=81.9138417082726x_{28} = 81.9138417082726
x29=72.4891426972687x_{29} = 72.4891426972687
x30=−42.180868035436x_{30} = -42.180868035436
x31=6.52244633170316x_{31} = 6.52244633170316
x32=−73.5962847878296x_{32} = -73.5962847878296
x33=22.2252019991699x_{33} = 22.2252019991699
x34=−92.4457015068628x_{34} = -92.4457015068628
x35=−48.46389829568x_{35} = -48.46389829568
x36=85.0554119241887x_{36} = 85.0554119241887
x37=28.5078993606643x_{37} = 28.5078993606643
x38=15.9428843727392x_{38} = 15.9428843727392
x39=−29.6150062107158x_{39} = -29.6150062107158
x40=−13.9089903135835x_{40} = -13.9089903135835
x41=97.621707199601x_{41} = 97.621707199601
x42=94.4801315058989x_{42} = 94.4801315058989
x43=59.9229158515985x_{43} = 59.9229158515985
Puntos máximos de la función:
x43=64.6352443879741x_{43} = 64.6352443879741
x43=−72.0255033591792x_{43} = -72.0255033591792
x43=−94.0164887583458x_{43} = -94.0164887583458
x43=−100.2996406125x_{43} = -100.2996406125
x43=45.7860045671659x_{43} = 45.7860045671659
x43=52.06905917643x_{43} = 52.06905917643
x43=20.6545735900731x_{43} = 20.6545735900731
x43=−21.7616436866734x_{43} = -21.7616436866734
x43=39.5029913226638x_{43} = 39.5029913226638
x43=58.3521418348081x_{43} = 58.3521418348081
x43=86.6261976410267x_{43} = 86.6261976410267
x43=1.82726394043287x_{43} = 1.82726394043287
x43=−78.308632669004x_{43} = -78.308632669004
x43=67.7768014012035x_{43} = 67.7768014012035
x43=80.3430572566921x_{43} = 80.3430572566921
x43=30.0786053386116x_{43} = 30.0786053386116
x43=14.3724218304636x_{43} = 14.3724218304636
x43=83.4846266056516x_{43} = 83.4846266056516
x43=61.4936910044344x_{43} = 61.4936910044344
x43=42.6444916370061x_{43} = 42.6444916370061
x43=17.5134060900679x_{43} = 17.5134060900679
x43=−50.0346619693212x_{43} = -50.0346619693212
x43=−81.4502005716198x_{43} = -81.4502005716198
x43=−59.4592803626043x_{43} = -59.4592803626043
x43=−28.0443057693738x_{43} = -28.0443057693738
x43=−12.33866578552x_{43} = -12.33866578552
x43=−37.4686296462638x_{43} = -37.4686296462638
x43=−6.05989325317838x_{43} = -6.05989325317838
x43=23.7958523877927x_{43} = 23.7958523877927
x43=−34.3271604895018x_{43} = -34.3271604895018
x43=96.0509192143605x_{43} = 96.0509192143605
x43=8.09183517436296x_{43} = 8.09183517436296
x43=−15.4794117940065x_{43} = -15.4794117940065
x43=−43.7516214066214x_{43} = -43.7516214066214
x43=−56.3177349431024x_{43} = -56.3177349431024
x43=−65.742384785425x_{43} = -65.742384785425
x43=89.7677701861569x_{43} = 89.7677701861569
x43=36.3615068758865x_{43} = 36.3615068758865
x43=−87.7333417066779x_{43} = -87.7333417066779
x43=74.0599244741303x_{43} = 74.0599244741303
x43=−122.290699217015x_{43} = -122.290699217015
Decrece en los intervalos
[100.763283948745,∞)\left[100.763283948745, \infty\right)
Crece en los intervalos
(−∞,−95.5872763087217]\left(-\infty, -95.5872763087217\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
4(5xsin⁡(2x)+10xcos⁡(2x)+7sin⁡(2x)−cos⁡(2x))e225=0\frac{4 \left(5 x \sin{\left(2 x \right)} + 10 x \cos{\left(2 x \right)} + 7 \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right) e^{2}}{25} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−52.39560050084x_{1} = -52.39560050084
x2=7.34011082755754x_{2} = 7.34011082755754
x3=90.5559181166057x_{3} = 90.5559181166057
x4=79.5607994828484x_{4} = 79.5607994828484
x5=−3.77823446654156x_{5} = -3.77823446654156
x6=76.4193610334537x_{6} = 76.4193610334537
x7=60.712407331793x_{7} = 60.712407331793
x8=−74.3850455717934x_{8} = -74.3850455717934
x9=−27.2681932185021x_{9} = -27.2681932185021
x10=98.4096364906533x_{10} = 98.4096364906533
x11=77.990078709455x_{11} = 77.990078709455
x12=63.853758468634x_{12} = 63.853758468634
x13=54.4297883675997x_{13} = 54.4297883675997
x14=−60.2488305449496x_{14} = -60.2488305449496
x15=−71.2436317213696x_{15} = -71.2436317213696
x16=−91.6630412793407x_{16} = -91.6630412793407
x17=12.0372918669791x_{17} = 12.0372918669791
x18=−83.8093677321176x_{18} = -83.8093677321176
x19=46.5767285387698x_{19} = 46.5767285387698
x20=−31.9789399874986x_{20} = -31.9789399874986
x21=82.7022496177044x_{21} = 82.7022496177044
x22=70.1365254526854x_{22} = 70.1365254526854
x23=49.7179176752173x_{23} = 49.7179176752173
x24=−63.3901748615295x_{24} = -63.3901748615295
x25=−33.54929194441x_{25} = -33.54929194441
x26=−90.0923022635643x_{26} = -90.0923022635643
x27=1.21743661824315x_{27} = 1.21743661824315
x28=−69.6729308591578x_{28} = -69.6729308591578
x29=10.4700863363716x_{29} = 10.4700863363716
x30=32.4423379871201x_{30} = 32.4423379871201
x31=5.77961404322637x_{31} = 5.77961404322637
x32=−39.8310517723009x_{32} = -39.8310517723009
x33=85.8437101583132x_{33} = 85.8437101583132
x34=62.2830798651494x_{34} = 62.2830798651494
x35=99.9803851183617x_{35} = 99.9803851183617
x36=27.7314984341647x_{36} = 27.7314984341647
x37=19.8817124115812x_{37} = 19.8817124115812
x38=−0.905837181017051x_{38} = -0.905837181017051
x39=143.961768689774x_{39} = 143.961768689774
x40=16.7428843878138x_{40} = 16.7428843878138
x41=104.692639572387x_{41} = 104.692639572387
x42=40.2945380022353x_{42} = 40.2945380022353
x43=−93.2337822301932x_{43} = -93.2337822301932
x44=−99.5167635483288x_{44} = -99.5167635483288
x45=68.5658265414413x_{45} = 68.5658265414413
x46=41.8650577909712x_{46} = 41.8650577909712
x47=−75.9557580572675x_{47} = -75.9557580572675
x48=−6.88153938882236x_{48} = -6.88153938882236
x49=13.605309684597x_{49} = 13.605309684597
x50=−5.32424319445369x_{50} = -5.32424319445369
x51=−68.102234412857x_{51} = -68.102234412857
x52=−17.8493252270127x_{52} = -17.8493252270127
x53=71.7072286191551x_{53} = 71.7072286191551
x54=26.161341533004x_{54} = 26.161341533004
x55=38.72404051969x_{55} = 38.72404051969
x56=93.6974001819511x_{56} = 93.6974001819511
x57=−16.280185477059x_{57} = -16.280185477059
x58=−96.3752695579269x_{58} = -96.3752695579269
x59=−19.4187349802935x_{59} = -19.4187349802935
x60=−77.5264739484552x_{60} = -77.5264739484552
x61=0.0409142048473795x_{61} = 0.0409142048473795
x62=−2.2657101507875x_{62} = -2.2657101507875
x63=−97.9460157604398x_{63} = -97.9460157604398
x64=18.3121814372645x_{64} = 18.3121814372645
x65=−38.2605677226714x_{65} = -38.2605677226714
x66=56.0004312402572x_{66} = 56.0004312402572
x67=−53.9662289489669x_{67} = -53.9662289489669
x68=−49.2543758469485x_{68} = -49.2543758469485
x69=−85.3800978970367x_{69} = -85.3800978970367
x70=−24.1280542185133x_{70} = -24.1280542185133
x71=−8.44388256158267x_{71} = -8.44388256158267
x72=−30.4086341979852x_{72} = -30.4086341979852
x73=84.272978659837x_{73} = 84.272978659837
x74=−41.4015596186877x_{74} = -41.4015596186877
x75=57.5710824552644x_{75} = 57.5710824552644
x76=4.22618247840335x_{76} = 4.22618247840335
x77=−61.8194995387526x_{77} = -61.8194995387526
x78=−25.6980790089547x_{78} = -25.6980790089547
x79=−46.1132015324485x_{79} = -46.1132015324485
x80=−55.5368669248221x_{80} = -55.5368669248221
x81=92.1266582086398x_{81} = 92.1266582086398
x82=−10.0088987328688x_{82} = -10.0088987328688
x83=24.5912655440908x_{83} = 24.5912655440908
x84=48.1473165545846x_{84} = 48.1473165545846
x85=35.5831242121309x_{85} = 35.5831242121309
x86=−11.575496705649x_{86} = -11.575496705649
x87=34.0127126021886x_{87} = 34.0127126021886
x88=−82.2386401004529x_{88} = -82.2386401004529
x89=−88.5215652860922x_{89} = -88.5215652860922
x90=−47.6837817731732x_{90} = -47.6837817731732

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
[143.961768689774,∞)\left[143.961768689774, \infty\right)
Convexa en los intervalos
(−∞,−99.5167635483288]\left(-\infty, -99.5167635483288\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=lim⁡x→−∞((−5xsin⁡(2x)+(−10xcos⁡(2x)+(3sin⁡(2x)−4cos⁡(2x))))e225)y = \lim_{x \to -\infty}\left(\frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2}}{25}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=lim⁡x→∞((−5xsin⁡(2x)+(−10xcos⁡(2x)+(3sin⁡(2x)−4cos⁡(2x))))e225)y = \lim_{x \to \infty}\left(\frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2}}{25}\right)
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función ((-4*cos(2*x) + 3*sin(2*x) - 10*x*cos(2*x) - 5*x*sin(2*x))*exp(2))/25, 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=xlim⁡x→−∞((−5xsin⁡(2x)+(−10xcos⁡(2x)+(3sin⁡(2x)−4cos⁡(2x))))e225x)y = x \lim_{x \to -\infty}\left(\frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2}}{25 x}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=xlim⁡x→∞((−5xsin⁡(2x)+(−10xcos⁡(2x)+(3sin⁡(2x)−4cos⁡(2x))))e225x)y = x \lim_{x \to \infty}\left(\frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2}}{25 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:
(−5xsin⁡(2x)+(−10xcos⁡(2x)+(3sin⁡(2x)−4cos⁡(2x))))e225=(−5xsin⁡(2x)+10xcos⁡(2x)−3sin⁡(2x)−4cos⁡(2x))e225\frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2}}{25} = \frac{\left(- 5 x \sin{\left(2 x \right)} + 10 x \cos{\left(2 x \right)} - 3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right) e^{2}}{25}
- No
(−5xsin⁡(2x)+(−10xcos⁡(2x)+(3sin⁡(2x)−4cos⁡(2x))))e225=−(−5xsin⁡(2x)+10xcos⁡(2x)−3sin⁡(2x)−4cos⁡(2x))e225\frac{\left(- 5 x \sin{\left(2 x \right)} + \left(- 10 x \cos{\left(2 x \right)} + \left(3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right)\right)\right) e^{2}}{25} = - \frac{\left(- 5 x \sin{\left(2 x \right)} + 10 x \cos{\left(2 x \right)} - 3 \sin{\left(2 x \right)} - 4 \cos{\left(2 x \right)}\right) e^{2}}{25}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор