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Trazado el gráfico de la función/ 2*cos(2*x-1)-8*x*sin(2*x-1)-4*x^2*cos(2*x-1)

Gráfico de la función y = 2*cos(2*x-1)-8*x*sin(2*x-1)-4*x^2*cos(2*x-1)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
                                              2             
f(x) = 2*cos(2*x - 1) - 8*x*sin(2*x - 1) - 4*x *cos(2*x - 1)
f(x)=−4x2cos⁡(2x−1)+(−8xsin⁡(2x−1)+2cos⁡(2x−1))f{\left(x \right)} = - 4 x^{2} \cos{\left(2 x - 1 \right)} + \left(- 8 x \sin{\left(2 x - 1 \right)} + 2 \cos{\left(2 x - 1 \right)}\right) 
f = -4*x^2*cos(2*x - 1) - 8*x*sin(2*x - 1) + 2*cos(2*x - 1)
Gráfico de la función
02468-8-6-4-2-1010-10001000
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:
−4x2cos⁡(2x−1)+(−8xsin⁡(2x−1)+2cos⁡(2x−1))=0- 4 x^{2} \cos{\left(2 x - 1 \right)} + \left(- 8 x \sin{\left(2 x - 1 \right)} + 2 \cos{\left(2 x - 1 \right)}\right) = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=−44.2902640560273x_{1} = -44.2902640560273
x2=−23.8891421475962x_{2} = -23.8891421475962
x3=92.4024062904502x_{3} = 92.4024062904502
x4=−47.4303637039338x_{4} = -47.4303637039338
x5=34.3012538612854x_{5} = 34.3012538612854
x6=−9.81123335736824x_{6} = -9.81123335736824
x7=12.3614330006265x_{7} = 12.3614330006265
x8=93.9730217922836x_{8} = 93.9730217922836
x9=65.7032645690185x_{9} = 65.7032645690185
x10=−22.3212723815348x_{10} = -22.3212723815348
x11=84.5494295060249x_{11} = 84.5494295060249
x12=−45.8602883655701x_{12} = -45.8602883655701
x13=70.4146357493599x_{13} = 70.4146357493599
x14=−83.5495709974012x_{14} = -83.5495709974012
x15=56.2810329045682x_{15} = 56.2810329045682
x16=10.8020992675291x_{16} = 10.8020992675291
x17=21.7516432728514x_{17} = 21.7516432728514
x18=−52.1408498931305x_{18} = -52.1408498931305
x19=−96.1143774302111x_{19} = -96.1143774302111
x20=62.5624355392392x_{20} = 62.5624355392392
x21=18.6177414772076x_{21} = 18.6177414772076
x22=−17.6207575392924x_{22} = -17.6207575392924
x23=−88.2613212434482x_{23} = -88.2613212434482
x24=51.5702655677765x_{24} = 51.5702655677765
x25=57.8513473083137x_{25} = 57.8513473083137
x26=−66.2739299165404x_{26} = -66.2739299165404
x27=20.1843963981734x_{27} = 20.1843963981734
x28=−33.3021266104817x_{28} = -33.3021266104817
x29=100.255540435733x_{29} = 100.255540435733
x30=29.5934911700293x_{30} = 29.5934911700293
x31=13.9232849104984x_{31} = 13.9232849104984
x32=87.6905986325861x_{32} = 87.6905986325861
x33=76.696658380699x_{33} = 76.696658380699
x34=−53.7110860299215x_{34} = -53.7110860299215
x35=24.8874700186884x_{35} = 24.8874700186884
x36=−30.1636505517863x_{36} = -30.1636505517863
x37=86.120010209162x_{37} = 86.120010209162
x38=7.69673291626194x_{38} = 7.69673291626194
x39=−58.4219749246612x_{39} = -58.4219749246612
x40=−69.4148401931228x_{40} = -69.4148401931228
x41=42.1498164383068x_{41} = 42.1498164383068
x42=3.15080352490827x_{42} = 3.15080352490827
x43=6.15679403890819x_{43} = 6.15679403890819
x44=−8.25901697833585x_{44} = -8.25901697833585
x45=40.5799365955341x_{45} = 40.5799365955341
x46=−97.6850065163975x_{46} = -97.6850065163975
x47=−0.0970399131642464x_{47} = -0.0970399131642464
x48=−81.9790038898832x_{48} = -81.9790038898832
x49=79.8377382709643x_{49} = 79.8377382709643
x50=−14.4913004307637x_{50} = -14.4913004307637
x51=78.2671931841158x_{51} = 78.2671931841158
x52=−67.8443771630354x_{52} = -67.8443771630354
x53=1.75404455752587x_{53} = 1.75404455752587
x54=−91.402524643265x_{54} = -91.402524643265
x55=98.6849028199871x_{55} = 98.6849028199871
x56=−59.9923235232566x_{56} = -59.9923235232566
x57=73.5556222564975x_{57} = 73.5556222564975
x58=−89.831919542018x_{58} = -89.831919542018
x59=−74.1263139634143x_{59} = -74.1263139634143
x60=−36.4411379958607x_{60} = -36.4411379958607
x61=−16.0554455931697x_{61} = -16.0554455931697
x62=50.0000776009994x_{62} = 50.0000776009994
x63=−31.7328117881048x_{63} = -31.7328117881048
x64=26.4558932611422x_{64} = 26.4558932611422
x65=−80.4084457319764x_{65} = -80.4084457319764
x66=4.63499042353007x_{66} = 4.63499042353007
x67=−77.2673584460767x_{67} = -77.2673584460767
x68=−2.24598929268983x_{68} = -2.24598929268983
x69=−61.5626949417979x_{69} = -61.5626949417979
x70=64.1328407126903x_{70} = 64.1328407126903
x71=−25.4573703720898x_{71} = -25.4573703720898
x72=−55.2813539533296x_{72} = -55.2813539533296
x73=48.4299290250951x_{73} = 48.4299290250951
x74=−99.2556408935399x_{74} = -99.2556408935399
x75=95.5436432368743x_{75} = 95.5436432368743
x76=−3.68364567757167x_{76} = -3.68364567757167
x77=54.7107461335906x_{77} = 54.7107461335906
x78=68.8441632221941x_{78} = 68.8441632221941
x79=71.9851223952702x_{79} = 71.9851223952702
x80=−11.3683760937863x_{80} = -11.3683760937863
x81=43.7197619754645x_{81} = 43.7197619754645
x82=−38.0108031609953x_{82} = -38.0108031609953
x83=32.7318522550145x_{83} = 32.7318522550145
x84=−39.580557838404x_{84} = -39.580557838404
x85=−75.6968305216214x_{85} = -75.6968305216214
x86=28.0245809007865x_{86} = 28.0245809007865
x87=15.4869130165443x_{87} = 15.4869130165443
x88=35.8707771682567x_{88} = 35.8707771682567
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 2*cos(2*x - 1) - 8*x*sin(2*x - 1) - 4*x^2*cos(2*x - 1).
−4⋅02cos⁡(−1+0⋅2)+(−0⋅8sin⁡(−1+0⋅2)+2cos⁡(−1+0⋅2))- 4 \cdot 0^{2} \cos{\left(-1 + 0 \cdot 2 \right)} + \left(- 0 \cdot 8 \sin{\left(-1 + 0 \cdot 2 \right)} + 2 \cos{\left(-1 + 0 \cdot 2 \right)}\right)
Resultado:
f(0)=2cos⁡(1)f{\left(0 \right)} = 2 \cos{\left(1 \right)}
Punto:
(0, 2*cos(1))
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
8x2sin⁡(2x−1)−24xcos⁡(2x−1)−12sin⁡(2x−1)=08 x^{2} \sin{\left(2 x - 1 \right)} - 24 x \cos{\left(2 x - 1 \right)} - 12 \sin{\left(2 x - 1 \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−13.7454424649031x_{1} = -13.7454424649031
x2=−78.0590278387603x_{2} = -78.0590278387603
x3=−54.5053777782732x_{3} = -54.5053777782732
x4=−100.045955778513x_{4} = -100.045955778513
x5=17.862344375829x_{5} = 17.862344375829
x6=−18.4305864331261x_{6} = -18.4305864331261
x7=−87.4817373771312x_{7} = -87.4817373771312
x8=46.0856186401591x_{8} = 46.0856186401591
x9=10.0715784898416x_{9} = 10.0715784898416
x10=−71.7775228591046x_{10} = -71.7775228591046
x11=−92.1932505821902x_{11} = -92.1932505821902
x12=−62.3558992621817x_{12} = -62.3558992621817
x13=−9.08696525527583x_{13} = -9.08696525527583
x14=94.7636058262731x_{14} = 94.7636058262731
x15=61.7853248233988x_{15} = 61.7853248233988
x16=30.3944015566408x_{16} = 30.3944015566408
x17=−65.4963397665622x_{17} = -65.4963397665622
x18=97.9046908873213x_{18} = 97.9046908873213
x19=2.56454858441185x_{19} = 2.56454858441185
x20=−98.475398463575x_{20} = -98.475398463575
x21=0.255057292795444x_{21} = 0.255057292795444
x22=−56.0754047130423x_{22} = -56.0754047130423
x23=−29.396069200616x_{23} = -29.396069200616
x24=8.52643161023247x_{24} = 8.52643161023247
x25=99.4752454314598x_{25} = 99.4752454314598
x26=−51.365464702974x_{26} = -51.365464702974
x27=25.6909954133979x_{27} = 25.6909954133979
x28=−40.3778194956686x_{28} = -40.3778194956686
x29=−41.9472296113986x_{29} = -41.9472296113986
x30=−10.6348026966634x_{30} = -10.6348026966634
x31=39.8075538658339x_{31} = 39.8075538658339
x32=13.1792214851291x_{32} = 13.1792214851291
x33=47.6553450518662x_{33} = 47.6553450518662
x34=91.6225555444572x_{34} = 91.6225555444572
x35=−15.3053493542512x_{35} = -15.3053493542512
x36=16.2994775253611x_{36} = 16.2994775253611
x37=44.5159674615453x_{37} = 44.5159674615453
x38=90.052044581842x_{38} = 90.052044581842
x39=−12.1882244212329x_{39} = -12.1882244212329
x40=33.5313975501223x_{40} = 33.5313975501223
x41=55.5048829432982x_{41} = 55.5048829432982
x42=−70.2071935402763x_{42} = -70.2071935402763
x43=5.47402786638968x_{43} = 5.47402786638968
x44=77.4883729226451x_{44} = 77.4883729226451
x45=60.2151607921807x_{45} = 60.2151607921807
x46=−34.1014490139235x_{46} = -34.1014490139235
x47=−57.645473480912x_{47} = -57.645473480912
x48=−1.71875795960904x_{48} = -1.71875795960904
x49=80.6292120555262x_{49} = 80.6292120555262
x50=24.1239643752974x_{50} = 24.1239643752974
x51=−76.4886257467472x_{51} = -76.4886257467472
x52=14.738250592123x_{52} = 14.738250592123
x53=69.63657212598x_{53} = 69.63657212598
x54=−19.9950915027445x_{54} = -19.9950915027445
x55=49.2251395274187x_{55} = 49.2251395274187
x56=68.0662722684833x_{56} = 68.0662722684833
x57=−7.54776657204502x_{57} = -7.54776657204502
x58=−27.8281322058858x_{58} = -27.8281322058858
x59=66.49599582797x_{59} = 66.49599582797
x60=75.9179767130818x_{60} = 75.9179767130818
x61=−48.2257698009748x_{61} = -48.2257698009748
x62=−67.0666004261986x_{62} = -67.0666004261986
x63=−85.9112543046859x_{63} = -85.9112543046859
x64=−49.7955874100927x_{64} = -49.7955874100927
x65=−84.340782888566x_{65} = -84.340782888566
x66=83.7701076430789x_{66} = 83.7701076430789
x67=−3.07154924173024x_{67} = -3.07154924173024
x68=−93.7637745287469x_{68} = -93.7637745287469
x69=−43.5167393888333x_{69} = -43.5167393888333
x70=−95.334307443617x_{70} = -95.334307443617
x71=−79.6294454655589x_{71} = -79.6294454655589
x72=58.6450305613792x_{72} = 58.6450305613792
x73=74.3475973883145x_{73} = 74.3475973883145
x74=31.9627874270162x_{74} = 31.9627874270162
x75=38.238299376953x_{75} = 38.238299376953
x76=88.4815437417652x_{76} = 88.4815437417652
x77=−37.2393483520332x_{77} = -37.2393483520332
x78=22.5574506870232x_{78} = 22.5574506870232
x79=−26.2605338391812x_{79} = -26.2605338391812
x80=−6.02278540107339x_{80} = -6.02278540107339
x81=−63.9261053849685x_{81} = -63.9261053849685
x82=52.3649082708794x_{82} = 52.3649082708794
x83=3.98814189957044x_{83} = 3.98814189957044
x84=−21.5604973394978x_{84} = -21.5604973394978
x85=11.6232273660655x_{85} = 11.6232273660655
x86=36.6691762860526x_{86} = 36.6691762860526
x87=−35.670317839542x_{87} = -35.670317839542
x88=96.3341442218117x_{88} = 96.3341442218117
x89=53.9348721067019x_{89} = 53.9348721067019
x90=−73.3478721519596x_{90} = -73.3478721519596
x91=82.199653196388x_{91} = 82.199653196388
Signos de extremos en los puntos:
(-13.745442464903133, 759.77147176229)

(-78.05902783876034, -24376.8480459664)

(-54.50537777827324, 11887.3463371545)

(-100.04595577851272, -40040.7735197272)

(17.862344375828997, 1280.2670996291)

(-18.43058643312613, -1362.75896762812)

(-87.4817373771312, -30616.218085395)

(46.085618640159076, 8499.539091591)

(10.07157848984163, -409.787418144425)

(-71.77752285910461, -20612.0520230781)

(-92.19325058219025, 34002.3823405188)

(-62.35589926218166, -15557.0338458372)

(-9.086965255275832, -334.340707861971)

(94.76360582627314, -35924.5644573929)

(61.78532482339878, 15273.7066301614)

(30.394401556640812, 3699.2834078743)

(-65.49633976656222, -17163.0831380772)

(97.9046908873213, -38345.3144599947)

(2.5645485844118494, 30.5121141140142)

(-98.47539846357498, 38793.6168738508)

(0.2550572927954443, 2.4952478331758)

(-56.07540471304232, -12581.80548193)

(-29.396069200615973, 3460.52069147914)

(8.526431610232473, 294.854960984045)

(99.47524543145977, 39585.2982689435)

(-51.365464702974, 10557.645556377)

(25.69099541339786, -2644.11570708713)

(-40.37781949566862, -6525.47597383058)

(-41.94722961139862, 7042.28283269147)

(-10.63480269666343, 456.432894004919)

(39.80755386583388, 6342.56820281612)

(13.17922148512906, -698.792125794266)

(47.655345051866156, -9088.12962169577)

(91.62255554445724, -33582.7712734673)

(-15.305349354251165, -941.033365595024)

(16.29947752536112, -1066.70824727944)

(44.51596746154533, -7930.68769667754)

(90.05204458184198, 32441.4834877784)

(-12.188224421232922, -598.239785904422)

(33.53139755012229, 4501.42245708499)

(55.504882943298156, 12327.1695786014)

(-70.20719354027626, 19720.2010104971)

(5.474027866389676, 123.972536245951)

(77.48837292264511, 24021.7925011179)

(60.21516079218075, -14507.4635949201)

(-34.10144901392346, -4655.63913920824)

(-57.645473480911974, 13296.0038018907)

(-1.7187579596090397, 15.8983270794995)

(80.62921205552618, 26008.2800380164)

(24.12396437529738, 2331.87024276556)

(-76.48862574674722, 23406.0402424856)

(14.738250592122988, 872.884003284896)

(69.63657212598, -19401.0096360852)

(-19.99509150274451, 1603.2257426745)

(49.225139527418655, 9696.45929620862)

(68.06627226848326, 18536.070651514)

(-7.547766572045018, 231.942817906739)

(-27.82813220588575, -3101.62551216705)

(66.49599582797003, -17690.8708602491)

(75.91797671308176, -23058.1575323844)

(-48.22576980097476, 9306.90141899861)

(-67.06660042619863, 17995.7165693708)

(-85.91125430468587, 29526.9750737694)

(-49.795587410092686, -9922.40391030186)

(-84.34078288856597, -28457.4712648369)

(83.77010764307893, 28073.7243785707)

(-3.0715492417302355, -41.9395531168933)

(-93.76377452874692, -35170.5821668367)

(-43.51673938883327, -7578.82879317638)

(-95.33430744361699, 36358.5211976505)

(-79.62944546555889, 25367.3950492875)

(58.64503056137922, 13760.9597431911)

(74.34759738831451, 22114.2617624372)

(31.962787427016163, -4090.48348660865)

(38.238299376953, -5852.67321572174)

(88.48154374176521, -31319.9349058306)

(-37.23934835203324, -5551.07948671938)

(22.55745068702316, -2039.3630150436)

(-26.26053383918125, 2762.46899101559)

(-6.022785401073386, -149.193422622551)

(-63.92610538496845, 16350.1888975129)

(52.36490827087939, 10972.3361085836)

(3.9881418995704365, -67.7882176786082)

(-21.56049733949778, -1863.42967748705)

(11.623227366065521, 544.428841150467)

(36.669176286052604, 5382.5172823381)

(-35.67031783954202, 5093.48981089821)

(96.33414422181174, 37125.0698562252)

(53.93487210670192, -11639.8832588279)

(-73.34787215195965, 21523.6422319283)

(82.19965319638801, -27031.1326075369)


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=−78.0590278387603x_{1} = -78.0590278387603
x2=−100.045955778513x_{2} = -100.045955778513
x3=−18.4305864331261x_{3} = -18.4305864331261
x4=−87.4817373771312x_{4} = -87.4817373771312
x5=10.0715784898416x_{5} = 10.0715784898416
x6=−71.7775228591046x_{6} = -71.7775228591046
x7=−62.3558992621817x_{7} = -62.3558992621817
x8=−9.08696525527583x_{8} = -9.08696525527583
x9=94.7636058262731x_{9} = 94.7636058262731
x10=−65.4963397665622x_{10} = -65.4963397665622
x11=97.9046908873213x_{11} = 97.9046908873213
x12=−56.0754047130423x_{12} = -56.0754047130423
x13=25.6909954133979x_{13} = 25.6909954133979
x14=−40.3778194956686x_{14} = -40.3778194956686
x15=13.1792214851291x_{15} = 13.1792214851291
x16=47.6553450518662x_{16} = 47.6553450518662
x17=91.6225555444572x_{17} = 91.6225555444572
x18=−15.3053493542512x_{18} = -15.3053493542512
x19=16.2994775253611x_{19} = 16.2994775253611
x20=44.5159674615453x_{20} = 44.5159674615453
x21=−12.1882244212329x_{21} = -12.1882244212329
x22=60.2151607921807x_{22} = 60.2151607921807
x23=−34.1014490139235x_{23} = -34.1014490139235
x24=69.63657212598x_{24} = 69.63657212598
x25=−27.8281322058858x_{25} = -27.8281322058858
x26=66.49599582797x_{26} = 66.49599582797
x27=75.9179767130818x_{27} = 75.9179767130818
x28=−49.7955874100927x_{28} = -49.7955874100927
x29=−84.340782888566x_{29} = -84.340782888566
x30=−3.07154924173024x_{30} = -3.07154924173024
x31=−93.7637745287469x_{31} = -93.7637745287469
x32=−43.5167393888333x_{32} = -43.5167393888333
x33=31.9627874270162x_{33} = 31.9627874270162
x34=38.238299376953x_{34} = 38.238299376953
x35=88.4815437417652x_{35} = 88.4815437417652
x36=−37.2393483520332x_{36} = -37.2393483520332
x37=22.5574506870232x_{37} = 22.5574506870232
x38=−6.02278540107339x_{38} = -6.02278540107339
x39=3.98814189957044x_{39} = 3.98814189957044
x40=−21.5604973394978x_{40} = -21.5604973394978
x41=53.9348721067019x_{41} = 53.9348721067019
x42=82.199653196388x_{42} = 82.199653196388
Puntos máximos de la función:
x42=−13.7454424649031x_{42} = -13.7454424649031
x42=−54.5053777782732x_{42} = -54.5053777782732
x42=17.862344375829x_{42} = 17.862344375829
x42=46.0856186401591x_{42} = 46.0856186401591
x42=−92.1932505821902x_{42} = -92.1932505821902
x42=61.7853248233988x_{42} = 61.7853248233988
x42=30.3944015566408x_{42} = 30.3944015566408
x42=2.56454858441185x_{42} = 2.56454858441185
x42=−98.475398463575x_{42} = -98.475398463575
x42=0.255057292795444x_{42} = 0.255057292795444
x42=−29.396069200616x_{42} = -29.396069200616
x42=8.52643161023247x_{42} = 8.52643161023247
x42=99.4752454314598x_{42} = 99.4752454314598
x42=−51.365464702974x_{42} = -51.365464702974
x42=−41.9472296113986x_{42} = -41.9472296113986
x42=−10.6348026966634x_{42} = -10.6348026966634
x42=39.8075538658339x_{42} = 39.8075538658339
x42=90.052044581842x_{42} = 90.052044581842
x42=33.5313975501223x_{42} = 33.5313975501223
x42=55.5048829432982x_{42} = 55.5048829432982
x42=−70.2071935402763x_{42} = -70.2071935402763
x42=5.47402786638968x_{42} = 5.47402786638968
x42=77.4883729226451x_{42} = 77.4883729226451
x42=−57.645473480912x_{42} = -57.645473480912
x42=−1.71875795960904x_{42} = -1.71875795960904
x42=80.6292120555262x_{42} = 80.6292120555262
x42=24.1239643752974x_{42} = 24.1239643752974
x42=−76.4886257467472x_{42} = -76.4886257467472
x42=14.738250592123x_{42} = 14.738250592123
x42=−19.9950915027445x_{42} = -19.9950915027445
x42=49.2251395274187x_{42} = 49.2251395274187
x42=68.0662722684833x_{42} = 68.0662722684833
x42=−7.54776657204502x_{42} = -7.54776657204502
x42=−48.2257698009748x_{42} = -48.2257698009748
x42=−67.0666004261986x_{42} = -67.0666004261986
x42=−85.9112543046859x_{42} = -85.9112543046859
x42=83.7701076430789x_{42} = 83.7701076430789
x42=−95.334307443617x_{42} = -95.334307443617
x42=−79.6294454655589x_{42} = -79.6294454655589
x42=58.6450305613792x_{42} = 58.6450305613792
x42=74.3475973883145x_{42} = 74.3475973883145
x42=−26.2605338391812x_{42} = -26.2605338391812
x42=−63.9261053849685x_{42} = -63.9261053849685
x42=52.3649082708794x_{42} = 52.3649082708794
x42=11.6232273660655x_{42} = 11.6232273660655
x42=36.6691762860526x_{42} = 36.6691762860526
x42=−35.670317839542x_{42} = -35.670317839542
x42=96.3341442218117x_{42} = 96.3341442218117
x42=−73.3478721519596x_{42} = -73.3478721519596
Decrece en los intervalos
[97.9046908873213,∞)\left[97.9046908873213, \infty\right)
Crece en los intervalos
(−∞,−100.045955778513]\left(-\infty, -100.045955778513\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
16(x2cos⁡(2x−1)+4xsin⁡(2x−1)−3cos⁡(2x−1))=016 \left(x^{2} \cos{\left(2 x - 1 \right)} + 4 x \sin{\left(2 x - 1 \right)} - 3 \cos{\left(2 x - 1 \right)}\right) = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=18.6705717423016x_{1} = 18.6705717423016
x2=−36.468459748885x_{2} = -36.468459748885
x3=−38.0370058872653x_{3} = -38.0370058872653
x4=76.7096838477643x_{4} = 76.7096838477643
x5=20.233244997467x_{5} = 20.233244997467
x6=−45.8820334925161x_{6} = -45.8820334925161
x7=7.81546868183201x_{7} = 7.81546868183201
x8=42.1734638137364x_{8} = 42.1734638137364
x9=50.0200310648299x_{9} = 50.0200310648299
x10=71.9989985425319x_{10} = 71.9989985425319
x11=−33.3319980042763x_{11} = -33.3319980042763
x12=13.9930378229993x_{12} = 13.9930378229993
x13=−25.4963028177509x_{13} = -25.4963028177509
x14=29.627059513409x_{14} = 29.627059513409
x15=73.5692027759837x_{15} = 73.5692027759837
x16=15.5499677482902x_{16} = 15.5499677482902
x17=−97.6952372496663x_{17} = -97.6952372496663
x18=−9.90748511222571x_{18} = -9.90748511222571
x19=−44.3127755353943x_{19} = -44.3127755353943
x20=84.5612472673631x_{20} = 84.5612472673631
x21=−66.2889988058797x_{21} = -66.2889988058797
x22=−31.7641439146333x_{22} = -31.7641439146333
x23=−80.4208710310574x_{23} = -80.4208710310574
x24=28.0600017191682x_{24} = 28.0600017191682
x25=21.7970601751647x_{25} = 21.7970601751647
x26=54.7289885609358x_{26} = 54.7289885609358
x27=87.7019937225293x_{27} = 87.7019937225293
x28=62.5783958024973x_{28} = 62.5783958024973
x29=−3.88201470954148x_{29} = -3.88201470954148
x30=65.7184639878592x_{30} = 65.7184639878592
x31=3.36471721533569x_{31} = 3.36471721533569
x32=−53.7296666265585x_{32} = -53.7296666265585
x33=56.2987682478699x_{33} = 56.2987682478699
x34=−11.4526164813365x_{34} = -11.4526164813365
x35=−60.0089653709625x_{35} = -60.0089653709625
x36=−0.171755521711389x_{36} = -0.171755521711389
x37=9.34793644726707x_{37} = 9.34793644726707
x38=70.4288206634315x_{38} = 70.4288206634315
x39=78.2799577798835x_{39} = 78.2799577798835
x40=6.29875868870323x_{40} = 6.29875868870323
x41=95.5541029760546x_{41} = 95.5541029760546
x42=43.7425654377933x_{42} = 43.7425654377933
x43=−83.5615299502453x_{43} = -83.5615299502453
x44=48.4505262488631x_{44} = 48.4505262488631
x45=57.8686029398956x_{45} = 57.8686029398956
x46=64.1484112801825x_{46} = 64.1484112801825
x47=−17.6764714380412x_{47} = -17.6764714380412
x48=−52.159987693273x_{48} = -52.159987693273
x49=100.265509162975x_{49} = 100.265509162975
x50=40.604492478675x_{50} = 40.604492478675
x51=−88.2726427600706x_{51} = -88.2726427600706
x52=−8.37089132860318x_{52} = -8.37089132860318
x53=93.983656121925x_{53} = 93.983656121925
x54=79.8502522286304x_{54} = 79.8502522286304
x55=−81.9911915609696x_{55} = -81.9911915609696
x56=37.4670055808895x_{56} = 37.4670055808895
x57=−67.8590981332547x_{57} = -67.8590981332547
x58=51.5896141927496x_{58} = 51.5896141927496
x59=−30.1965924906014x_{59} = -30.1965924906014
x60=−69.4292289252849x_{60} = -69.4292289252849
x61=86.1316127902409x_{61} = 86.1316127902409
x62=−63.1489039032174x_{62} = -63.1489039032174
x63=12.4394060869237x_{63} = 12.4394060869237
x64=−47.4513927846913x_{64} = -47.4513927846913
x65=35.8985294751837x_{65} = 35.8985294751837
x66=−58.4390625915167x_{66} = -58.4390625915167
x67=−75.7100276858897x_{67} = -75.7100276858897
x68=−61.5789136008956x_{68} = -61.5789136008956
x69=−91.4134576289256x_{69} = -91.4134576289256
x70=−77.2802878948122x_{70} = -77.2802878948122
x71=26.4933808444353x_{71} = 26.4933808444353
x72=−96.1247751372719x_{72} = -96.1247751372719
x73=−99.2657099273654x_{73} = -99.2657099273654
x74=−39.6057292112229x_{74} = -39.6057292112229
x75=34.3302638318207x_{75} = 34.3302638318207
x76=−5.34593825108834x_{76} = -5.34593825108834
x77=−23.9305806883344x_{77} = -23.9305806883344
x78=92.4132211331571x_{78} = 92.4132211331571
x79=98.6950300179717x_{79} = 98.6950300179717
x80=−19.238267249357x_{80} = -19.238267249357
x81=2.00709382868363x_{81} = 2.00709382868363
x82=−22.3655571311011x_{82} = -22.3655571311011
x83=−89.8430434044416x_{83} = -89.8430434044416
x84=−16.1163659673146x_{84} = -16.1163659673146
x85=−55.2994088042838x_{85} = -55.2994088042838
x86=−74.1397901501143x_{86} = -74.1397901501143
x87=10.8903627987145x_{87} = 10.8903627987145

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
[100.265509162975,∞)\left[100.265509162975, \infty\right)
Convexa en los intervalos
(−∞,−97.6952372496663]\left(-\infty, -97.6952372496663\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→−∞(−4x2cos⁡(2x−1)+(−8xsin⁡(2x−1)+2cos⁡(2x−1)))y = \lim_{x \to -\infty}\left(- 4 x^{2} \cos{\left(2 x - 1 \right)} + \left(- 8 x \sin{\left(2 x - 1 \right)} + 2 \cos{\left(2 x - 1 \right)}\right)\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=lim⁡x→∞(−4x2cos⁡(2x−1)+(−8xsin⁡(2x−1)+2cos⁡(2x−1)))y = \lim_{x \to \infty}\left(- 4 x^{2} \cos{\left(2 x - 1 \right)} + \left(- 8 x \sin{\left(2 x - 1 \right)} + 2 \cos{\left(2 x - 1 \right)}\right)\right)
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función 2*cos(2*x - 1) - 8*x*sin(2*x - 1) - 4*x^2*cos(2*x - 1), 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→−∞(−4x2cos⁡(2x−1)+(−8xsin⁡(2x−1)+2cos⁡(2x−1))x)y = x \lim_{x \to -\infty}\left(\frac{- 4 x^{2} \cos{\left(2 x - 1 \right)} + \left(- 8 x \sin{\left(2 x - 1 \right)} + 2 \cos{\left(2 x - 1 \right)}\right)}{x}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=xlim⁡x→∞(−4x2cos⁡(2x−1)+(−8xsin⁡(2x−1)+2cos⁡(2x−1))x)y = x \lim_{x \to \infty}\left(\frac{- 4 x^{2} \cos{\left(2 x - 1 \right)} + \left(- 8 x \sin{\left(2 x - 1 \right)} + 2 \cos{\left(2 x - 1 \right)}\right)}{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:
−4x2cos⁡(2x−1)+(−8xsin⁡(2x−1)+2cos⁡(2x−1))=−4x2cos⁡(2x+1)−8xsin⁡(2x+1)+2cos⁡(2x+1)- 4 x^{2} \cos{\left(2 x - 1 \right)} + \left(- 8 x \sin{\left(2 x - 1 \right)} + 2 \cos{\left(2 x - 1 \right)}\right) = - 4 x^{2} \cos{\left(2 x + 1 \right)} - 8 x \sin{\left(2 x + 1 \right)} + 2 \cos{\left(2 x + 1 \right)}
- No
−4x2cos⁡(2x−1)+(−8xsin⁡(2x−1)+2cos⁡(2x−1))=4x2cos⁡(2x+1)+8xsin⁡(2x+1)−2cos⁡(2x+1)- 4 x^{2} \cos{\left(2 x - 1 \right)} + \left(- 8 x \sin{\left(2 x - 1 \right)} + 2 \cos{\left(2 x - 1 \right)}\right) = 4 x^{2} \cos{\left(2 x + 1 \right)} + 8 x \sin{\left(2 x + 1 \right)} - 2 \cos{\left(2 x + 1 \right)}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор