Sr Examen

Otras calculadoras

  • ¿Cómo usar?

  • Gráfico de la función y =:
  • x^3+3*x^2+2 x^3+3*x^2+2
  • -sqrt(3*x+1) -sqrt(3*x+1)
  • -sqrt(1-x^2) -sqrt(1-x^2)
  • x^2/(4-x^2) x^2/(4-x^2)

  • Expresiones idénticas

  • uno /3cos(x/ dos)+cos5x
  • 1 dividir por 3 coseno de (x dividir por 2) más coseno de 5x
  • uno dividir por 3 coseno de (x dividir por dos) más coseno de 5x
  • 1/3cosx/2+cos5x
  • 1 dividir por 3cos(x dividir por 2)+cos5x

  • Expresiones semejantes

  • 1/3cos(x/2)-cos5x
Trazado el gráfico de la función/ 1/3cos(x/2)+cos5x

Gráfico de la función y = 1/3cos(x/2)+cos5x

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
          /x\           
       cos|-|           
          \2/           
f(x) = ------ + cos(5*x)
         3
f(x)=cos⁡(5x)+cos⁡(x2)3f{\left(x \right)} = \cos{\left(5 x \right)} + \frac{\cos{\left(\frac{x}{2} \right)}}{3} 
f = cos(5*x) + cos(x/2)/3
Gráfico de la función
02468-8-6-4-2-10102.5-2.5
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:
cos⁡(5x)+cos⁡(x2)3=0\cos{\left(5 x \right)} + \frac{\cos{\left(\frac{x}{2} \right)}}{3} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=−97.6934309417684x_{1} = -97.6934309417684
x2=29.8938872709176x_{2} = 29.8938872709176
x3=46.2109055982426x_{3} = 46.2109055982426
x4=−85.1270603274092x_{4} = -85.1270603274092
x5=0.380849905394364x_{5} = 0.380849905394364
x6=54.3200593166308x_{6} = 54.3200593166308
x7=−71.9316825098295x_{7} = -71.9316825098295
x8=−63.7130784359822x_{8} = -63.7130784359822
x9=100.150115009479x_{9} = 100.150115009479
x10=−80.1593697283543x_{10} = -80.1593697283543
x11=−11.6851452501728x_{11} = -11.6851452501728
x12=−38.0799617484719x_{12} = -38.0799617484719
x13=6.03645629423459x_{13} = 6.03645629423459
x14=−36.0818660562827x_{14} = -36.0818660562827
x15=43.7355681373121x_{15} = 43.7355681373121
x16=−64.4490988585907x_{16} = -64.4490988585907
x17=44.2290261632021x_{17} = 44.2290261632021
x18=53.1030164305417x_{18} = 53.1030164305417
x19=−19.851377041101x_{19} = -19.851377041101
x20=48.0976879663392x_{20} = 48.0976879663392
x21=49.8846325520423x_{21} = 49.8846325520423
x22=17.8477348019765x_{22} = 17.8477348019765
x23=26.0139665929047x_{23} = 26.0139665929047
x24=−14.7341651054567x_{24} = -14.7341651054567
x25=−21.6662000523928x_{25} = -21.6662000523928
x26=−7.80522457215995x_{26} = -7.80522457215995
x27=39.866906334175x_{27} = 39.866906334175
x28=−75.7790735915494x_{28} = -75.7790735915494
x29=−87.5837443951199x_{29} = -87.5837443951199
x30=78.23575765926x_{30} = 78.23575765926
x31=71.9316825098295x_{31} = 71.9316825098295
x32=−4.05457685919406x_{32} = -4.05457685919406
x33=14.183616401154x_{33} = 14.183616401154
x34=−85.7967998094167x_{34} = -85.7967998094167
x35=−83.9100174413202x_{35} = -83.9100174413202
x36=−39.866906334175x_{36} = -39.866906334175
x37=83.9100174413202x_{37} = 83.9100174413202
x38=−27.9702752018233x_{38} = -27.9702752018233
x39=76.2794490503414x_{39} = 76.2794490503414
x40=−53.7320236337622x_{40} = -53.7320236337622
x41=68.1132172594132x_{41} = 68.1132172594132
x42=−31.6626555488429x_{42} = -31.6626555488429
x43=38.0799617484719x_{43} = 38.0799617484719
x44=80.1593697283543x_{44} = 80.1593697283543
x45=81.9281380062796x_{45} = 81.9281380062796
x46=92.0191711597083x_{46} = 92.0191711597083
x47=−94.0010505947488x_{47} = -94.0010505947488
x48=12.1855207089648x_{48} = 12.1855207089648
x49=22.2952072556133x_{49} = 22.2952072556133
x50=−43.7355681373121x_{50} = -43.7355681373121
x51=59.9943190986909x_{51} = 59.9943190986909
x52=27.9702752018233x_{52} = 27.9702752018233
x53=90.1323887916117x_{53} = 90.1323887916117
x54=56.3019387516713x_{54} = 56.3019387516713
x55=−81.9281380062796x_{55} = -81.9281380062796
x56=−16.0329117906847x_{56} = -16.0329117906847
x57=−48.6482366706419x_{57} = -48.6482366706419
x58=−95.7698188726742x_{58} = -95.7698188726742
x59=88.3454442059086x_{59} = 88.3454442059086
x60=16.0329117906847x_{60} = 16.0329117906847
x61=4.05457685919406x_{61} = 4.05457685919406
x62=34.232570666752x_{62} = 34.232570666752
x63=75.0173737807607x_{63} = 75.0173737807607
x64=−65.6693870449009x_{64} = -65.6693870449009
x65=2.837533973105x_{65} = 2.837533973105
x66=36.0818660562827x_{66} = 36.0818660562827
x67=−49.8846325520423x_{67} = -49.8846325520423
x68=86.3473485137194x_{68} = 86.3473485137194
x69=−58.0707070295966x_{69} = -58.0707070295966
x70=235.923507699719x_{70} = 235.923507699719
x71=21.6662000523928x_{71} = 21.6662000523928
x72=2.16779449109753x_{72} = 2.16779449109753
x73=94.0010505947488x_{73} = 94.0010505947488
x74=−51.8827282442315x_{74} = -51.8827282442315
x75=−17.8477348019765x_{75} = -17.8477348019765
x76=70.1168594985377x_{76} = 70.1168594985377
x77=−92.0191711597083x_{77} = -92.0191711597083
x78=10.3985761232616x_{78} = 10.3985761232616
x79=−26.0139665929047x_{79} = -26.0139665929047
x80=98.3631704237759x_{80} = 98.3631704237759
x81=−73.7809778993602x_{81} = -73.7809778993602
x82=66.2983942481214x_{82} = 66.2983942481214
x83=32.4177476554601x_{83} = 32.4177476554601
x84=−61.9506277076095x_{84} = -61.9506277076095
x85=58.0707070295966x_{85} = 58.0707070295966
x86=24.251515864532x_{86} = 24.251515864532
x87=−9.72883664125417x_{87} = -9.72883664125417
x88=−59.9943190986909x_{88} = -59.9943190986909
x89=−53.1030164305417x_{89} = -53.1030164305417
x90=−33.6445349838835x_{90} = -33.6445349838835
x91=−70.1168594985377x_{91} = -70.1168594985377
x92=−48.0976879663392x_{92} = -48.0976879663392
x93=61.9506277076095x_{93} = 61.9506277076095
x94=−6.03645629423459x_{94} = -6.03645629423459
x95=−41.7536887022716x_{95} = -41.7536887022716
x96=−29.8938872709176x_{96} = -29.8938872709176
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/2)/3 + cos(5*x).
cos⁡(02)3+cos⁡(0⋅5)\frac{\cos{\left(\frac{0}{2} \right)}}{3} + \cos{\left(0 \cdot 5 \right)}
Resultado:
f(0)=43f{\left(0 \right)} = \frac{4}{3}
Punto:
(0, 4/3)
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
−5sin⁡(5x)−sin⁡(x2)6=0- 5 \sin{\left(5 x \right)} - \frac{\sin{\left(\frac{x}{2} \right)}}{6} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=99.9005796833491x_{1} = 99.9005796833491
x2=76.0286089176793x_{2} = 76.0286089176793
x3=8.16275737000355x_{3} = 8.16275737000355
x4=89.2173230918662x_{4} = 89.2173230918662
x5=272.696590280948x_{5} = 272.696590280948
x6=42.1027250874331x_{6} = 42.1027250874331
x7=−27.6396804726839x_{7} = -27.6396804726839
x8=−43.9822971502571x_{8} = -43.9822971502571
x9=−3.76356323495361x_{9} = -3.76356323495361
x10=−37.6991118430775x_{10} = -37.6991118430775
x11=−52.7724217014022x_{11} = -52.7724217014022
x12=−77.9051629301206x_{12} = -77.9051629301206
x13=67.2354663161515x_{13} = 67.2354663161515
x14=5.02261883564151x_{14} = 5.02261883564151
x15=−20.1101223930768x_{15} = -20.1101223930768
x16=64.0845818631479x_{16} = 64.0845818631479
x17=72.2499631677839x_{17} = 72.2499631677839
x18=33.9355486081239x_{18} = 33.9355486081239
x19=−42.1027250874331x_{19} = -42.1027250874331
x20=26.3854700200704x_{20} = 26.3854700200704
x21=50.2654824574367x_{21} = 50.2654824574367
x22=−65.980113590167x_{22} = -65.980113590167
x23=−45.8618692130811x_{23} = -45.8618692130811
x24=−87.9645943005142x_{24} = -87.9645943005142
x25=−32.0421914287363x_{25} = -32.0421914287363
x26=−5.6569204143412x_{26} = -5.6569204143412
x27=40.2060510870431x_{27} = 40.2060510870431
x28=38.3294970746018x_{28} = 38.3294970746018
x29=48.3751221912863x_{29} = 48.3751221912863
x30=52.1558427235871x_{30} = 52.1558427235871
x31=77.9051629301206x_{31} = 77.9051629301206
x32=1.89036026615036x_{32} = 1.89036026615036
x33=60.3249138278303x_{33} = 60.3249138278303
x34=55.9224028717779x_{34} = 55.9224028717779
x35=−25.7631264602426x_{35} = -25.7631264602426
x36=11.3136418230072x_{36} = 11.3136418230072
x37=−99.9005796833491x_{37} = -99.9005796833491
x38=−10.0594313703936x_{38} = -10.0594313703936
x39=−33.9355486081239x_{39} = -33.9355486081239
x40=84.2010310655606x_{40} = 84.2010310655606
x41=94.2477796076938x_{41} = 94.2477796076938
x42=−79.8018369305107x_{42} = -79.8018369305107
x43=−54.0290456923903x_{43} = -54.0290456923903
x44=−96.1273516705178x_{44} = -96.1273516705178
x45=96.1273516705178x_{45} = 96.1273516705178
x46=70.3756048505135x_{46} = 70.3756048505135
x47=6.28318530717959x_{47} = 6.28318530717959
x48=−35.8087515769272x_{48} = -35.8087515769272
x49=−64.0845818631479x_{49} = -64.0845818631479
x50=74.145494894803x_{50} = 74.145494894803
x51=32.0421914287363x_{51} = 32.0421914287363
x52=61.5791242804438x_{52} = 61.5791242804438
x53=21.9844807103472x_{53} = 21.9844807103472
x54=−55.9224028717779x_{54} = -55.9224028717779
x55=82.307673886173x_{55} = 82.307673886173
x56=−98.0240256709078x_{56} = -98.0240256709078
x57=23.8800124373663x_{57} = 23.8800124373663
x58=−21.9844807103472x_{58} = -21.9844807103472
x59=−69.7413032718138x_{59} = -69.7413032718138
x60=−86.0742340343638x_{60} = -86.0742340343638
x61=28.2810017470895x_{61} = 28.2810017470895
x62=0x_{62} = 0
x63=65.980113590167x_{63} = 65.980113590167
x64=62.2014678402716x_{64} = 62.2014678402716
x65=−93.6215147148554x_{65} = -93.6215147148554
x66=45.8618692130811x_{66} = 45.8618692130811
x67=18.2232910287004x_{67} = 18.2232910287004
x68=−71.6346604512014x_{68} = -71.6346604512014
x69=−67.8544719074374x_{69} = -67.8544719074374
x70=−47.7585432134711x_{70} = -47.7585432134711
x71=−76.0286089176793x_{71} = -76.0286089176793
x72=16.3299338493128x_{72} = 16.3299338493128
x73=−23.8800124373663x_{73} = -23.8800124373663
x74=11.9359853828349x_{74} = 11.9359853828349
x75=−57.8092342361544x_{75} = -57.8092342361544
x76=−13.8190994057112x_{76} = -13.8190994057112
x77=−49.6350972259124x_{77} = -49.6350972259124
x78=10.0594313703936x_{78} = 10.0594313703936
x79=−74.145494894803x_{79} = -74.145494894803
x80=98.0240256709078x_{80} = 98.0240256709078
x81=−15.7146311327303x_{81} = -15.7146311327303
x82=−9.41811009598804x_{82} = -9.41811009598804
x83=20.1101223930768x_{83} = 20.1101223930768
x84=87.9645943005142x_{84} = 87.9645943005142
x85=−84.8163337821431x_{85} = -84.8163337821431
x86=−59.6835925534247x_{86} = -59.6835925534247
x87=43.9822971502571x_{87} = 43.9822971502571
x88=−81.6814089933346x_{88} = -81.6814089933346
x89=−1.89036026615036x_{89} = -1.89036026615036
x90=54.0290456923903x_{90} = 54.0290456923903
x91=−39.5894721092279x_{91} = -39.5894721092279
x92=−89.8549545666646x_{92} = -89.8549545666646
x93=−91.7281575354678x_{93} = -91.7281575354678
x94=−19.4758208143771x_{94} = -19.4758208143771
x95=−11.9359853828349x_{95} = -11.9359853828349
x96=92.3682075448698x_{96} = 92.3682075448698
x97=86.0742340343638x_{97} = 86.0742340343638
x98=30.1553600643599x_{98} = 30.1553600643599
Signos de extremos en los puntos:
(99.90057968334914, -0.683034381241965)

(76.02860891767929, -0.683034381241964)

(8.162757370003554, -1.19629134322177)

(89.21732309186623, 1.2698637607974)

(272.6965902809482, 0.897497398652965)

(42.102725087433136, -1.19629134322177)

(-27.639680472683892, 1.1035076926828)

(-43.982297150257104, 0.666666666666667)

(-3.7635632349536086, 0.897497398652963)

(-37.69911184307752, 1.33333333333333)

(-52.77242170140224, 1.1035076926828)

(-77.90516293012058, 1.1035076926828)

(67.23546631615149, -1.19629134322177)

(5.022618835641509, 0.730520133233146)

(-20.110122393076836, 0.730520133233146)

(64.08458186314787, 1.2698637607974)

(72.2499631677839, -1.0005556049543)

(33.93554860812391, 0.897497398652963)

(-42.102725087433136, -1.19629134322177)

(26.38547002007036, 1.2698637607974)

(50.26548245743669, 1.33333333333333)

(-65.98011359016701, -1.0005556049543)

(-45.86186921308107, -1.19629134322177)

(-87.96459430051421, 1.33333333333333)

(-32.04219142873632, -1.31707172239489)

(-5.656920414341204, -1.31707172239489)

(40.206051087043065, 1.1035076926828)

(38.329497074601775, -0.683034381241965)

(48.37512219128633, -0.804435933553383)

(52.15584272358706, -0.804435933553383)

(77.90516293012058, 1.1035076926828)

(1.8903602661503636, -0.804435933553383)

(60.324913827830315, 1.1035076926828)

(55.9224028717779, -1.31707172239489)

(-25.7631264602426, -0.683034381241965)

(11.313641823007156, 1.2698637607974)

(-99.90057968334914, -0.683034381241965)

(-10.059431370393625, 1.1035076926828)

(-33.93554860812391, 0.897497398652963)

(84.2010310655606, 0.897497398652963)

(94.2477796076938, 0.666666666666667)

(-79.80183693051066, -1.19629134322177)

(-54.0290456923903, 0.897497398652963)

(-96.12735167051777, -1.19629134322177)

(96.12735167051777, -1.19629134322177)

(70.37560485051353, 0.730520133233146)

(6.283185307179586, 0.666666666666667)

(-35.80875157692716, -0.804435933553383)

(-64.08458186314787, 1.2698637607974)

(74.14549489480302, 1.2698637607974)

(32.04219142873632, -1.31707172239489)

(61.57912428044385, 1.2698637607974)

(21.98448071034721, -1.0005556049543)

(-55.9224028717779, -1.31707172239489)

(82.307673886173, -1.31707172239489)

(-98.02402567090783, 1.1035076926828)

(23.88001243736633, 1.2698637607974)

(-21.98448071034721, -1.0005556049543)

(-69.74130327181383, -1.31707172239489)

(-86.07423403436384, -0.804435933553383)

(28.281001747089483, -1.0005556049543)

(0, 4/3)

(65.98011359016701, -1.0005556049543)

(62.20146784027161, -0.683034381241965)

(-93.62151471485542, -1.31707172239489)

(45.86186921308107, -1.19629134322177)

(18.223291028700377, -1.31707172239489)

(-71.63466045120143, 0.897497398652964)

(-67.85447190743737, 0.730520133233145)

(-47.75854321347114, 1.1035076926828)

(-76.02860891767929, -0.683034381241964)

(16.32993384931278, 0.897497398652963)

(-23.88001243736633, 1.2698637607974)

(11.93598538283492, -0.683034381241965)

(-57.80923423615435, 0.730520133233146)

(-13.81909940571119, 1.2698637607974)

(-49.63509722591244, -0.683034381241965)

(10.059431370393625, 1.1035076926828)

(-74.14549489480302, 1.2698637607974)

(98.02402567090783, 1.1035076926828)

(-15.71463113273031, -1.0005556049543)

(-9.418110095988036, -1.0005556049543)

(20.110122393076836, 0.730520133233146)

(87.96459430051421, 1.33333333333333)

(-84.81633378214308, -1.0005556049543)

(-59.68359255342473, -1.0005556049543)

(43.982297150257104, 0.666666666666667)

(-81.68140899333463, 0.666666666666667)

(-1.8903602661503636, -0.804435933553383)

(54.0290456923903, 0.897497398652963)

(-39.589472109227884, -0.804435933553384)

(-89.85495456666457, -0.804435933553384)

(-91.72815753546782, 0.897497398652962)

(-19.47582081437714, -1.31707172239489)

(-11.93598538283492, -0.683034381241965)

(92.36820754486983, -1.19629134322177)

(86.07423403436384, -0.804435933553383)

(30.155360064359854, 0.730520133233146)


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=99.9005796833491x_{1} = 99.9005796833491
x2=76.0286089176793x_{2} = 76.0286089176793
x3=8.16275737000355x_{3} = 8.16275737000355
x4=42.1027250874331x_{4} = 42.1027250874331
x5=67.2354663161515x_{5} = 67.2354663161515
x6=72.2499631677839x_{6} = 72.2499631677839
x7=−42.1027250874331x_{7} = -42.1027250874331
x8=−65.980113590167x_{8} = -65.980113590167
x9=−45.8618692130811x_{9} = -45.8618692130811
x10=−32.0421914287363x_{10} = -32.0421914287363
x11=−5.6569204143412x_{11} = -5.6569204143412
x12=38.3294970746018x_{12} = 38.3294970746018
x13=48.3751221912863x_{13} = 48.3751221912863
x14=52.1558427235871x_{14} = 52.1558427235871
x15=1.89036026615036x_{15} = 1.89036026615036
x16=55.9224028717779x_{16} = 55.9224028717779
x17=−25.7631264602426x_{17} = -25.7631264602426
x18=−99.9005796833491x_{18} = -99.9005796833491
x19=−79.8018369305107x_{19} = -79.8018369305107
x20=−96.1273516705178x_{20} = -96.1273516705178
x21=96.1273516705178x_{21} = 96.1273516705178
x22=−35.8087515769272x_{22} = -35.8087515769272
x23=32.0421914287363x_{23} = 32.0421914287363
x24=21.9844807103472x_{24} = 21.9844807103472
x25=−55.9224028717779x_{25} = -55.9224028717779
x26=82.307673886173x_{26} = 82.307673886173
x27=−21.9844807103472x_{27} = -21.9844807103472
x28=−69.7413032718138x_{28} = -69.7413032718138
x29=−86.0742340343638x_{29} = -86.0742340343638
x30=28.2810017470895x_{30} = 28.2810017470895
x31=65.980113590167x_{31} = 65.980113590167
x32=62.2014678402716x_{32} = 62.2014678402716
x33=−93.6215147148554x_{33} = -93.6215147148554
x34=45.8618692130811x_{34} = 45.8618692130811
x35=18.2232910287004x_{35} = 18.2232910287004
x36=−76.0286089176793x_{36} = -76.0286089176793
x37=11.9359853828349x_{37} = 11.9359853828349
x38=−49.6350972259124x_{38} = -49.6350972259124
x39=−15.7146311327303x_{39} = -15.7146311327303
x40=−9.41811009598804x_{40} = -9.41811009598804
x41=−84.8163337821431x_{41} = -84.8163337821431
x42=−59.6835925534247x_{42} = -59.6835925534247
x43=−1.89036026615036x_{43} = -1.89036026615036
x44=−39.5894721092279x_{44} = -39.5894721092279
x45=−89.8549545666646x_{45} = -89.8549545666646
x46=−19.4758208143771x_{46} = -19.4758208143771
x47=−11.9359853828349x_{47} = -11.9359853828349
x48=92.3682075448698x_{48} = 92.3682075448698
x49=86.0742340343638x_{49} = 86.0742340343638
Puntos máximos de la función:
x49=89.2173230918662x_{49} = 89.2173230918662
x49=272.696590280948x_{49} = 272.696590280948
x49=−27.6396804726839x_{49} = -27.6396804726839
x49=−43.9822971502571x_{49} = -43.9822971502571
x49=−3.76356323495361x_{49} = -3.76356323495361
x49=−37.6991118430775x_{49} = -37.6991118430775
x49=−52.7724217014022x_{49} = -52.7724217014022
x49=−77.9051629301206x_{49} = -77.9051629301206
x49=5.02261883564151x_{49} = 5.02261883564151
x49=−20.1101223930768x_{49} = -20.1101223930768
x49=64.0845818631479x_{49} = 64.0845818631479
x49=33.9355486081239x_{49} = 33.9355486081239
x49=26.3854700200704x_{49} = 26.3854700200704
x49=50.2654824574367x_{49} = 50.2654824574367
x49=−87.9645943005142x_{49} = -87.9645943005142
x49=40.2060510870431x_{49} = 40.2060510870431
x49=77.9051629301206x_{49} = 77.9051629301206
x49=60.3249138278303x_{49} = 60.3249138278303
x49=11.3136418230072x_{49} = 11.3136418230072
x49=−10.0594313703936x_{49} = -10.0594313703936
x49=−33.9355486081239x_{49} = -33.9355486081239
x49=84.2010310655606x_{49} = 84.2010310655606
x49=94.2477796076938x_{49} = 94.2477796076938
x49=−54.0290456923903x_{49} = -54.0290456923903
x49=70.3756048505135x_{49} = 70.3756048505135
x49=6.28318530717959x_{49} = 6.28318530717959
x49=−64.0845818631479x_{49} = -64.0845818631479
x49=74.145494894803x_{49} = 74.145494894803
x49=61.5791242804438x_{49} = 61.5791242804438
x49=−98.0240256709078x_{49} = -98.0240256709078
x49=23.8800124373663x_{49} = 23.8800124373663
x49=0x_{49} = 0
x49=−71.6346604512014x_{49} = -71.6346604512014
x49=−67.8544719074374x_{49} = -67.8544719074374
x49=−47.7585432134711x_{49} = -47.7585432134711
x49=16.3299338493128x_{49} = 16.3299338493128
x49=−23.8800124373663x_{49} = -23.8800124373663
x49=−57.8092342361544x_{49} = -57.8092342361544
x49=−13.8190994057112x_{49} = -13.8190994057112
x49=10.0594313703936x_{49} = 10.0594313703936
x49=−74.145494894803x_{49} = -74.145494894803
x49=98.0240256709078x_{49} = 98.0240256709078
x49=20.1101223930768x_{49} = 20.1101223930768
x49=87.9645943005142x_{49} = 87.9645943005142
x49=43.9822971502571x_{49} = 43.9822971502571
x49=−81.6814089933346x_{49} = -81.6814089933346
x49=54.0290456923903x_{49} = 54.0290456923903
x49=−91.7281575354678x_{49} = -91.7281575354678
x49=30.1553600643599x_{49} = 30.1553600643599
Decrece en los intervalos
[99.9005796833491,∞)\left[99.9005796833491, \infty\right)
Crece en los intervalos
(−∞,−99.9005796833491]\left(-\infty, -99.9005796833491\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
−(cos⁡(x2)12+25cos⁡(5x))=0- (\frac{\cos{\left(\frac{x}{2} \right)}}{12} + 25 \cos{\left(5 x \right)}) = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−21.6768849857751x_{1} = -21.6768849857751
x2=34.2432556001343x_{2} = 34.2432556001343
x3=93.9342788367197x_{3} = 93.9342788367197
x4=−73.8269560655013x_{4} = -73.8269560655013
x5=14.1376382350129x_{5} = 14.1376382350129
x6=32.3589982472937x_{6} = 32.3589982472937
x7=−97.7034272713185x_{7} = -97.7034272713185
x8=49.9506647663638x_{8} = 49.9506647663638
x9=−39.8979239502275x_{9} = -39.8979239502275
x10=5.96968453620544x_{10} = 5.96968453620544
x11=−19.7926276329346x_{11} = -19.7926276329346
x12=4.08376787908574x_{12} = 4.08376787908574
x13=10.3675585072091x_{13} = 10.3675585072091
x14=24.1908575277429x_{14} = 24.1908575277429
x15=83.8808264214285x_{15} = 83.8808264214285
x16=12.2515529232863x_{16} = 12.2515529232863
x17=80.1110841826216x_{17} = 80.1110841826216
x18=58.1189925753293x_{18} = 58.1189925753293
x19=−58.1189925753293x_{19} = -58.1189925753293
x20=−36.1278442224238x_{20} = -36.1278442224238
x21=−43.668796379283x_{21} = -43.668796379283
x22=71.9423674432118x_{22} = 71.9423674432118
x23=39.8979239502275x_{23} = 39.8979239502275
x24=88.2794119915871x_{24} = 88.2794119915871
x25=17.906484210143x_{25} = 17.906484210143
x26=2.19881210715002x_{26} = 2.19881210715002
x27=92.0483621795999x_{27} = 92.0483621795999
x28=0.314817691072884x_{28} = 0.314817691072884
x29=56.2351669936421x_{29} = 56.2351669936421
x30=61.8899693708204x_{30} = 61.8899693708204
x31=−26.0746249296938x_{31} = -26.0746249296938
x32=7.22625701857539x_{32} = 7.22625701857539
x33=46.181714578351x_{33} = 46.181714578351
x34=54.3492503365224x_{34} = 54.3492503365224
x35=−61.8899693708204x_{35} = -61.8899693708204
x36=−33.6153439639918x_{36} = -33.6153439639918
x37=39.2703794637313x_{37} = 39.2703794637313
x38=−65.6593907153507x_{38} = -65.6593907153507
x39=−7.85351011789259x_{39} = -7.85351011789259
x40=36.1278442224238x_{40} = 36.1278442224238
x41=−38.0139295341504x_{41} = -38.0139295341504
x42=100.216147223801x_{42} = 100.216147223801
x43=68.1719666675797x_{43} = 68.1719666675797
x44=−49.9506647663638x_{44} = -49.9506647663638
x45=−53.7213387003799x_{45} = -53.7213387003799
x46=93.304707896298x_{46} = 93.304707896298
x47=−17.906484210143x_{47} = -17.906484210143
x48=81.9949097643088x_{48} = 81.9949097643088
x49=22.3052035851635x_{49} = 22.3052035851635
x50=−81.9949097643088x_{50} = -81.9949097643088
x51=28.5885974716616x_{51} = 28.5885974716616
x52=−53.0930201009915x_{52} = -53.0930201009915
x53=−48.0666703502867x_{53} = -48.0666703502867
x54=−93.9342788367197x_{54} = -93.9342788367197
x55=65.0306651789459x_{55} = 65.0306651789459
x56=−85.7657821933642x_{56} = -85.7657821933642
x57=38.0139295341504x_{57} = 38.0139295341504
x58=−16.0222268573024x_{58} = -16.0222268573024
x59=48.0666703502867x_{59} = 48.0666703502867
x60=−71.9423674432118x_{60} = -71.9423674432118
x61=−92.0483621795999x_{61} = -92.0483621795999
x62=−87.6497766094413x_{62} = -87.6497766094413
x63=−83.8808264214285x_{63} = -83.8808264214285
x64=66.2877093147391x_{64} = 66.2877093147391
x65=76.3401073871305x_{65} = 76.3401073871305
x66=78.2257613297099x_{66} = 78.2257613297099
x67=−11.6244869133837x_{67} = -11.6244869133837
x68=16.0222268573024x_{68} = 16.0222268573024
x69=−51.8367500780904x_{69} = -51.8367500780904
x70=−60.004315428241x_{70} = -60.004315428241
x71=72.5706860426002x_{71} = 72.5706860426002
x72=1.57126762065375x_{72} = 1.57126762065375
x73=98.3321528077234x_{73} = 98.3321528077234
x74=−69.4285391499496x_{74} = -69.4285391499496
x75=−75.7130413772279x_{75} = -75.7130413772279
x76=90.1634064076642x_{76} = 90.1634064076642
x77=−27.9602788722732x_{77} = -27.9602788722732
x78=−80.1110841826216x_{78} = -80.1110841826216
x79=26.0746249296938x_{79} = 26.0746249296938
x80=21.0489733496326x_{80} = 21.0489733496326
x81=−5.96968453620544x_{81} = -5.96968453620544
x82=27.9602788722732x_{82} = 27.9602788722732
x83=−31.7294273068721x_{83} = -31.7294273068721
x84=70.0581100903712x_{84} = 70.0581100903712
x85=−95.8181044184068x_{85} = -95.8181044184068
x86=−14.1376382350129x_{86} = -14.1376382350129
x87=−9.73883297080434x_{87} = -9.73883297080434
x88=−70.0581100903712x_{88} = -70.0581100903712
x89=−63.7737367727714x_{89} = -63.7737367727714
x90=−41.7828797221633x_{90} = -41.7828797221633
x91=60.004315428241x_{91} = 60.004315428241
x92=−4.08376787908574x_{92} = -4.08376787908574
x93=−76.9694913068088x_{93} = -76.9694913068088
x94=44.2957979212313x_{94} = 44.2957979212313
x95=−29.8456017251849x_{95} = -29.8456017251849

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
[98.3321528077234,∞)\left[98.3321528077234, \infty\right)
Convexa en los intervalos
(−∞,−97.7034272713185]\left(-\infty, -97.7034272713185\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(cos⁡(5x)+cos⁡(x2)3)=⟨−43,43⟩\lim_{x \to -\infty}\left(\cos{\left(5 x \right)} + \frac{\cos{\left(\frac{x}{2} \right)}}{3}\right) = \left\langle - \frac{4}{3}, \frac{4}{3}\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=⟨−43,43⟩y = \left\langle - \frac{4}{3}, \frac{4}{3}\right\rangle
lim⁡x→∞(cos⁡(5x)+cos⁡(x2)3)=⟨−43,43⟩\lim_{x \to \infty}\left(\cos{\left(5 x \right)} + \frac{\cos{\left(\frac{x}{2} \right)}}{3}\right) = \left\langle - \frac{4}{3}, \frac{4}{3}\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=⟨−43,43⟩y = \left\langle - \frac{4}{3}, \frac{4}{3}\right\rangle
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función cos(x/2)/3 + cos(5*x), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(cos⁡(5x)+cos⁡(x2)3x)=0\lim_{x \to -\infty}\left(\frac{\cos{\left(5 x \right)} + \frac{\cos{\left(\frac{x}{2} \right)}}{3}}{x}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
lim⁡x→∞(cos⁡(5x)+cos⁡(x2)3x)=0\lim_{x \to \infty}\left(\frac{\cos{\left(5 x \right)} + \frac{\cos{\left(\frac{x}{2} \right)}}{3}}{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:
cos⁡(5x)+cos⁡(x2)3=cos⁡(x2)3+cos⁡(5x)\cos{\left(5 x \right)} + \frac{\cos{\left(\frac{x}{2} \right)}}{3} = \frac{\cos{\left(\frac{x}{2} \right)}}{3} + \cos{\left(5 x \right)}
- No
cos⁡(5x)+cos⁡(x2)3=−cos⁡(x2)3−cos⁡(5x)\cos{\left(5 x \right)} + \frac{\cos{\left(\frac{x}{2} \right)}}{3} = - \frac{\cos{\left(\frac{x}{2} \right)}}{3} - \cos{\left(5 x \right)}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор