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y=(x+3)cosx
Trazado el gráfico de la función/ y=(x+3)cosx

Gráfico de la función y = y=(x+3)cosx

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
f(x) = (x + 3)*cos(x)
f(x)=(x+3)cos⁡(x)f{\left(x \right)} = \left(x + 3\right) \cos{\left(x \right)} 
f = (x + 3)*cos(x)
Gráfico de la función
02468-8-6-4-2-1010-2525
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:
(x+3)cos⁡(x)=0\left(x + 3\right) \cos{\left(x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=−3x_{1} = -3
x2=−π2x_{2} = - \frac{\pi}{2}
x3=π2x_{3} = \frac{\pi}{2}
Solución numérica
x1=−29.845130209103x_{1} = -29.845130209103
x2=−67.5442420521806x_{2} = -67.5442420521806
x3=−70.6858347057703x_{3} = -70.6858347057703
x4=64.4026493985908x_{4} = 64.4026493985908
x5=−36.1283155162826x_{5} = -36.1283155162826
x6=−92.6769832808989x_{6} = -92.6769832808989
x7=−61.261056745001x_{7} = -61.261056745001
x8=−76.9690200129499x_{8} = -76.9690200129499
x9=−98.9601685880785x_{9} = -98.9601685880785
x10=−95.8185759344887x_{10} = -95.8185759344887
x11=29.845130209103x_{11} = 29.845130209103
x12=80.1106126665397x_{12} = 80.1106126665397
x13=−64.4026493985908x_{13} = -64.4026493985908
x14=36.1283155162826x_{14} = 36.1283155162826
x15=73.8274273593601x_{15} = 73.8274273593601
x16=32.9867228626928x_{16} = 32.9867228626928
x17=−4.71238898038469x_{17} = -4.71238898038469
x18=−39.2699081698724x_{18} = -39.2699081698724
x19=26.7035375555132x_{19} = 26.7035375555132
x20=−7.85398163397448x_{20} = -7.85398163397448
x21=95.8185759344887x_{21} = 95.8185759344887
x22=−17.2787595947439x_{22} = -17.2787595947439
x23=−10.9955742875643x_{23} = -10.9955742875643
x24=98.9601685880785x_{24} = 98.9601685880785
x25=−86.3937979737193x_{25} = -86.3937979737193
x26=92.6769832808989x_{26} = 92.6769832808989
x27=−48.6946861306418x_{27} = -48.6946861306418
x28=54.9778714378214x_{28} = 54.9778714378214
x29=45.553093477052x_{29} = 45.553093477052
x30=23.5619449019235x_{30} = 23.5619449019235
x31=76.9690200129499x_{31} = 76.9690200129499
x32=−89.5353906273091x_{32} = -89.5353906273091
x33=4.71238898038469x_{33} = 4.71238898038469
x34=−26.7035375555132x_{34} = -26.7035375555132
x35=−80.1106126665397x_{35} = -80.1106126665397
x36=7.85398163397448x_{36} = 7.85398163397448
x37=14.1371669411541x_{37} = 14.1371669411541
x38=86.3937979737193x_{38} = 86.3937979737193
x39=−45.553093477052x_{39} = -45.553093477052
x40=−83.2522053201295x_{40} = -83.2522053201295
x41=70.6858347057703x_{41} = 70.6858347057703
x42=83.2522053201295x_{42} = 83.2522053201295
x43=48.6946861306418x_{43} = 48.6946861306418
x44=−20.4203522483337x_{44} = -20.4203522483337
x45=51.8362787842316x_{45} = 51.8362787842316
x46=10.9955742875643x_{46} = 10.9955742875643
x47=−3x_{47} = -3
x48=20.4203522483337x_{48} = 20.4203522483337
x49=1.5707963267949x_{49} = 1.5707963267949
x50=89.5353906273091x_{50} = 89.5353906273091
x51=17.2787595947439x_{51} = 17.2787595947439
x52=58.1194640914112x_{52} = 58.1194640914112
x53=61.261056745001x_{53} = 61.261056745001
x54=−32.9867228626928x_{54} = -32.9867228626928
x55=−51.8362787842316x_{55} = -51.8362787842316
x56=−14.1371669411541x_{56} = -14.1371669411541
x57=−58.1194640914112x_{57} = -58.1194640914112
x58=−42.4115008234622x_{58} = -42.4115008234622
x59=−54.9778714378214x_{59} = -54.9778714378214
x60=−1.5707963267949x_{60} = -1.5707963267949
x61=42.4115008234622x_{61} = 42.4115008234622
x62=39.2699081698724x_{62} = 39.2699081698724
x63=67.5442420521806x_{63} = 67.5442420521806
x64=−102.101761241668x_{64} = -102.101761241668
x65=−23.5619449019235x_{65} = -23.5619449019235
x66=−73.8274273593601x_{66} = -73.8274273593601
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 (x + 3)*cos(x).
3cos⁡(0)3 \cos{\left(0 \right)}
Resultado:
f(0)=3f{\left(0 \right)} = 3
Punto:
(0, 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
−(x+3)sin⁡(x)+cos⁡(x)=0- \left(x + 3\right) \sin{\left(x \right)} + \cos{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−59.7078928202273x_{1} = -59.7078928202273
x2=84.8343862178182x_{2} = 84.8343862178182
x3=−97.3999650893223x_{3} = -97.3999650893223
x4=−87.9763617358531x_{4} = -87.9763617358531
x5=59.7062064512464x_{5} = 59.7062064512464
x6=−100.541216632062x_{6} = -100.541216632062
x7=−37.7278991803885x_{7} = -37.7278991803885
x8=−56.567333690088x_{8} = -56.567333690088
x9=34.5841198954721x_{9} = 34.5841198954721
x10=3.29903328785148x_{10} = 3.29903328785148
x11=−50.2866269338091x_{11} = -50.2866269338091
x12=−47.1465377637573x_{12} = -47.1465377637573
x13=−40.8671065042713x_{13} = -40.8671065042713
x14=−72.2710660715932x_{14} = -72.2710660715932
x15=31.4449502153243x_{15} = 31.4449502153243
x16=−81.6941157398245x_{16} = -81.6941157398245
x17=−25.1778008415242x_{17} = -25.1778008415242
x18=−94.2587370240534x_{18} = -94.2587370240534
x19=47.1438297937958x_{19} = 47.1438297937958
x20=−44.0066785894522x_{20} = -44.0066785894522
x21=91.1168116486103x_{21} = 91.1168116486103
x22=97.3993321575476x_{22} = 97.3993321575476
x23=−75.4120326678904x_{23} = -75.4120326678904
x24=50.2842475271843x_{24} = 50.2842475271843
x25=75.4109763113185x_{25} = 75.4109763113185
x26=94.2580611694573x_{26} = 94.2580611694573
x27=78.5520778284944x_{27} = 78.5520778284944
x28=40.8634985472455x_{28} = 40.8634985472455
x29=−91.1175349460173x_{29} = -91.1175349460173
x30=−15.786014834861x_{30} = -15.786014834861
x31=−12.6694230459213x_{31} = -12.6694230459213
x32=−9.57569676385338x_{32} = -9.57569676385338
x33=−28.3138174685366x_{33} = -28.3138174685366
x34=−34.5891650451544x_{34} = -34.5891650451544
x35=−18.912317780113x_{35} = -18.912317780113
x36=−69.130158920116x_{36} = -69.130158920116
x37=87.9755858178486x_{37} = 87.9755858178486
x38=−22.0436114382877x_{38} = -22.0436114382877
x39=−65.9893200989848x_{39} = -65.9893200989848
x40=−78.5530512997373x_{40} = -78.5530512997373
x41=−3.95172192033919x_{41} = -3.95172192033919
x42=37.7236626573345x_{42} = 37.7236626573345
x43=−53.4269031964768x_{43} = -53.4269031964768
x44=0.294682454486773x_{44} = 0.294682454486773
x45=56.5654544420077x_{45} = 56.5654544420077
x46=213.632916514985x_{46} = 213.632916514985
x47=15.7612143304042x_{47} = 15.7612143304042
x48=−2.22814103089124x_{48} = -2.22814103089124
x49=53.4247959606036x_{49} = 53.4247959606036
x50=6.38928965648362x_{50} = 6.38928965648362
x51=28.30626551274x_{51} = 28.30626551274
x52=100.540622659664x_{52} = 100.540622659664
x53=72.2699157713744x_{53} = 72.2699157713744
x54=22.0310776789363x_{54} = 22.0310776789363
x55=25.1682273173293x_{55} = 25.1682273173293
x56=−6.55723006500106x_{56} = -6.55723006500106
x57=9.50457883886398x_{57} = 9.50457883886398
x58=69.1289015588518x_{58} = 69.1289015588518
x59=−31.4510601479335x_{59} = -31.4510601479335
x60=−62.8485603567807x_{60} = -62.8485603567807
x61=18.8951963232073x_{61} = 18.8951963232073
x62=12.6302619891586x_{62} = 12.6302619891586
x63=−84.835220716198x_{63} = -84.835220716198
x64=44.0035689215071x_{64} = 44.0035689215071
x65=65.9879399974437x_{65} = 65.9879399974437
x66=62.8470386162472x_{66} = 62.8470386162472
x67=81.6932157658594x_{67} = 81.6932157658594
Signos de extremos en los puntos:
(-59.707892820227336, 56.6990777612809)

(84.83438621781819, -87.828694239774)

(-97.39996508932231, 94.3946689229274)

(-87.97636173585312, -84.9704783576549)

(59.70620645124642, -62.6982342794497)

(-100.54121663206242, -97.5360909979324)

(-37.7278991803885, -34.7135104817292)

(-56.56733369008799, -53.558002082243)

(34.58411989547207, -37.5708234637983)

(3.299033287851476, -6.22112560417095)

(-50.28662693380906, -47.2760566650762)

(-47.14653776375731, 44.1352162039481)

(-40.867106504271284, 37.8539093345704)

(-72.2710660715932, 69.2638491787087)

(31.444950215324322, 34.4304434690237)

(-81.69411573982451, -78.6877627940051)

(-25.177800841524213, -22.15529009427)

(-94.25873702405337, -91.2532585899567)

(47.14382979379579, -50.1338614505173)

(-44.006678589452186, -40.9944908893309)

(91.1168116486103, -94.1114995512231)

(97.39933215754765, -100.394352415252)

(-75.41203266789043, -72.4051287256054)

(50.28424752718431, 53.2748663689057)

(75.41097631131846, 78.4046004308088)

(94.25806116945732, 97.2529206150062)

(78.55207782849438, -81.545947468169)

(40.863498547245456, -43.8521039892383)

(-91.11753494601734, 88.1118612545098)

(-15.786014834860985, 12.7470881005591)

(-12.669423045921281, -9.61812478108002)

(-9.575696763853385, 6.50095316217611)

(-28.31381746853661, 25.2940884985806)

(-34.589165045154424, 31.5733487197023)

(-18.91231778011301, -15.8809883513863)

(-69.13015892011602, -66.1225993697551)

(87.97558581784861, 90.9700903358314)

(-22.043611438287677, 19.0174100876084)

(-65.98932009898483, 62.9813837455716)

(-78.55305129973732, 75.5464343027166)

(-3.951721920339186, 0.656121661044172)

(37.72366265733454, 40.7113903330478)

(-53.42690319647679, 50.4169907777953)

(0.2946824544867733, 3.15266324719375)

(56.56545444200766, 59.5570620887982)

(213.6329165149846, 216.630608500037)

(15.761214330404183, -18.7346202562976)

(-2.228141030891238, -0.471618974793956)

(53.424795960603625, -56.4159366951519)

(6.389289656483623, 9.33648628773909)

(28.30626551273998, -31.2903064803893)

(100.5406226596642, 103.535793974935)

(72.26991577137444, -75.2632738904155)

(22.031077678936263, -25.0111263891723)

(25.168227317329272, 28.1504935824352)

(-6.557230065001062, -3.42448900708588)

(9.504578838863976, -12.4647842585051)

(69.1289015588518, 72.121970523981)

(-31.45106014793351, -28.4335023766721)

(-62.84856035678067, -59.840207685858)

(18.895196323207266, 21.8723959280207)

(12.63026198915859, 15.59837063305)

(-84.83522071619804, 81.8291115616385)

(44.00356892150712, 46.9929350411195)

(65.98793999744368, -68.9806934957898)

(62.84703861624724, 65.8394465735594)

(81.69321576585943, 84.6873127224841)


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=84.8343862178182x_{1} = 84.8343862178182
x2=−87.9763617358531x_{2} = -87.9763617358531
x3=59.7062064512464x_{3} = 59.7062064512464
x4=−100.541216632062x_{4} = -100.541216632062
x5=−37.7278991803885x_{5} = -37.7278991803885
x6=−56.567333690088x_{6} = -56.567333690088
x7=34.5841198954721x_{7} = 34.5841198954721
x8=3.29903328785148x_{8} = 3.29903328785148
x9=−50.2866269338091x_{9} = -50.2866269338091
x10=−81.6941157398245x_{10} = -81.6941157398245
x11=−25.1778008415242x_{11} = -25.1778008415242
x12=−94.2587370240534x_{12} = -94.2587370240534
x13=47.1438297937958x_{13} = 47.1438297937958
x14=−44.0066785894522x_{14} = -44.0066785894522
x15=91.1168116486103x_{15} = 91.1168116486103
x16=97.3993321575476x_{16} = 97.3993321575476
x17=−75.4120326678904x_{17} = -75.4120326678904
x18=78.5520778284944x_{18} = 78.5520778284944
x19=40.8634985472455x_{19} = 40.8634985472455
x20=−12.6694230459213x_{20} = -12.6694230459213
x21=−18.912317780113x_{21} = -18.912317780113
x22=−69.130158920116x_{22} = -69.130158920116
x23=15.7612143304042x_{23} = 15.7612143304042
x24=−2.22814103089124x_{24} = -2.22814103089124
x25=53.4247959606036x_{25} = 53.4247959606036
x26=28.30626551274x_{26} = 28.30626551274
x27=72.2699157713744x_{27} = 72.2699157713744
x28=22.0310776789363x_{28} = 22.0310776789363
x29=−6.55723006500106x_{29} = -6.55723006500106
x30=9.50457883886398x_{30} = 9.50457883886398
x31=−31.4510601479335x_{31} = -31.4510601479335
x32=−62.8485603567807x_{32} = -62.8485603567807
x33=65.9879399974437x_{33} = 65.9879399974437
Puntos máximos de la función:
x33=−59.7078928202273x_{33} = -59.7078928202273
x33=−97.3999650893223x_{33} = -97.3999650893223
x33=−47.1465377637573x_{33} = -47.1465377637573
x33=−40.8671065042713x_{33} = -40.8671065042713
x33=−72.2710660715932x_{33} = -72.2710660715932
x33=31.4449502153243x_{33} = 31.4449502153243
x33=50.2842475271843x_{33} = 50.2842475271843
x33=75.4109763113185x_{33} = 75.4109763113185
x33=94.2580611694573x_{33} = 94.2580611694573
x33=−91.1175349460173x_{33} = -91.1175349460173
x33=−15.786014834861x_{33} = -15.786014834861
x33=−9.57569676385338x_{33} = -9.57569676385338
x33=−28.3138174685366x_{33} = -28.3138174685366
x33=−34.5891650451544x_{33} = -34.5891650451544
x33=87.9755858178486x_{33} = 87.9755858178486
x33=−22.0436114382877x_{33} = -22.0436114382877
x33=−65.9893200989848x_{33} = -65.9893200989848
x33=−78.5530512997373x_{33} = -78.5530512997373
x33=−3.95172192033919x_{33} = -3.95172192033919
x33=37.7236626573345x_{33} = 37.7236626573345
x33=−53.4269031964768x_{33} = -53.4269031964768
x33=0.294682454486773x_{33} = 0.294682454486773
x33=56.5654544420077x_{33} = 56.5654544420077
x33=213.632916514985x_{33} = 213.632916514985
x33=6.38928965648362x_{33} = 6.38928965648362
x33=100.540622659664x_{33} = 100.540622659664
x33=25.1682273173293x_{33} = 25.1682273173293
x33=69.1289015588518x_{33} = 69.1289015588518
x33=18.8951963232073x_{33} = 18.8951963232073
x33=12.6302619891586x_{33} = 12.6302619891586
x33=−84.835220716198x_{33} = -84.835220716198
x33=44.0035689215071x_{33} = 44.0035689215071
x33=62.8470386162472x_{33} = 62.8470386162472
x33=81.6932157658594x_{33} = 81.6932157658594
Decrece en los intervalos
[97.3993321575476,∞)\left[97.3993321575476, \infty\right)
Crece en los intervalos
(−∞,−100.541216632062]\left(-\infty, -100.541216632062\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
−((x+3)cos⁡(x)+2sin⁡(x))=0- (\left(x + 3\right) \cos{\left(x \right)} + 2 \sin{\left(x \right)}) = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−14.3121594602206x_{1} = -14.3121594602206
x2=−42.462138986437x_{2} = -42.462138986437
x3=−33.053173593001x_{3} = -33.053173593001
x4=92.6978793436777x_{4} = 92.6978793436777
x5=−86.4177690883985x_{5} = -86.4177690883985
x6=−23.6584567792085x_{6} = -23.6584567792085
x7=−17.4166086363428x_{7} = -17.4166086363428
x8=70.7129603215986x_{8} = 70.7129603215986
x9=58.1521577434381x_{9} = 58.1521577434381
x10=−95.8401150148972x_{10} = -95.8401150148972
x11=20.5052352226731x_{11} = 20.5052352226731
x12=−61.2953513467577x_{12} = -61.2953513467577
x13=−64.4351925360079x_{13} = -64.4351925360079
x14=55.0123332166132x_{14} = 55.0123332166132
x15=−55.0163019917346x_{15} = -55.0163019917346
x16=−48.7383852414105x_{16} = -48.7383852414105
x17=−11.2338590161227x_{17} = -11.2338590161227
x18=1.95446769860329x_{18} = 1.95446769860329
x19=29.9058350256858x_{19} = 29.9058350256858
x20=51.8727106470714x_{20} = 51.8727106470714
x21=26.770617096282x_{21} = 26.770617096282
x22=−73.8556462692966x_{22} = -73.8556462692966
x23=73.8534450440396x_{23} = 73.8534450440396
x24=−39.3249112691049x_{24} = -39.3249112691049
x25=89.5569955724082x_{25} = 89.5569955724082
x26=17.3765980243604x_{26} = 17.3765980243604
x27=36.1793185853157x_{27} = 36.1793185853157
x28=8.03330382965524x_{28} = 8.03330382965524
x29=80.1346653801375x_{29} = 80.1346653801375
x30=−5.40591660043711x_{30} = -5.40591660043711
x31=45.5942274137072x_{31} = 45.5942274137072
x32=−80.1365349095748x_{32} = -80.1365349095748
x33=−89.5584922796575x_{33} = -89.5584922796575
x34=76.9940166753296x_{34} = 76.9940166753296
x35=86.4161615658675x_{35} = 86.4161615658675
x36=11.136122961567x_{36} = 11.136122961567
x37=−58.1557091900213x_{37} = -58.1557091900213
x38=95.8388081401923x_{38} = 95.8388081401923
x39=−98.9810030297478x_{39} = -98.9810030297478
x40=−36.1885045575189x_{40} = -36.1885045575189
x41=−92.6992763110302x_{41} = -92.6992763110302
x42=−70.7153615177027x_{42} = -70.7153615177027
x43=61.2921547109207x_{43} = 61.2921547109207
x44=14.2525765162628x_{44} = 14.2525765162628
x45=39.3171352054588x_{45} = 39.3171352054588
x46=83.2753827526075x_{46} = 83.2753827526075
x47=−67.5752037953155x_{47} = -67.5752037953155
x48=−20.5339259723255x_{48} = -20.5339259723255
x49=98.9797778056003x_{49} = 98.9797778056003
x50=−3.09441845244876x_{50} = -3.09441845244876
x51=4.9585915020369x_{51} = 4.9585915020369
x52=64.432300083121x_{52} = 64.432300083121
x53=−76.996041906774x_{53} = -76.996041906774
x54=−83.2771138683158x_{54} = -83.2771138683158
x55=48.7333266866217x_{55} = 48.7333266866217
x56=33.0421565872763x_{56} = 33.0421565872763
x57=−8.21987886514604x_{57} = -8.21987886514604
x58=67.5725740899573x_{58} = 67.5725740899573
x59=23.6368881258944x_{59} = 23.6368881258944
x60=−45.6000073775805x_{60} = -45.6000073775805
x61=−29.9192901213547x_{61} = -29.9192901213547
x62=42.4554715670068x_{62} = 42.4554715670068
x63=−0.826862867228188x_{63} = -0.826862867228188
x64=−51.8771748648305x_{64} = -51.8771748648305
x65=−26.7874183328987x_{65} = -26.7874183328987

Intervalos de convexidad y concavidad:
Hallemos los intervales donde la función es convexa o cóncava, para eso veamos cómo se comporta la función en los puntos de flexiones:
Cóncava en los intervalos
[95.8388081401923,∞)\left[95.8388081401923, \infty\right)
Convexa en los intervalos
(−∞,−95.8401150148972]\left(-\infty, -95.8401150148972\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞((x+3)cos⁡(x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(\left(x + 3\right) \cos{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=⟨−∞,∞⟩y = \left\langle -\infty, \infty\right\rangle
lim⁡x→∞((x+3)cos⁡(x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(\left(x + 3\right) \cos{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=⟨−∞,∞⟩y = \left\langle -\infty, \infty\right\rangle
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función (x + 3)*cos(x), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞((x+3)cos⁡(x)x)=⟨−1,1⟩\lim_{x \to -\infty}\left(\frac{\left(x + 3\right) \cos{\left(x \right)}}{x}\right) = \left\langle -1, 1\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=⟨−1,1⟩xy = \left\langle -1, 1\right\rangle x
lim⁡x→∞((x+3)cos⁡(x)x)=⟨−1,1⟩\lim_{x \to \infty}\left(\frac{\left(x + 3\right) \cos{\left(x \right)}}{x}\right) = \left\langle -1, 1\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=⟨−1,1⟩xy = \left\langle -1, 1\right\rangle x
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:
(x+3)cos⁡(x)=(3−x)cos⁡(x)\left(x + 3\right) \cos{\left(x \right)} = \left(3 - x\right) \cos{\left(x \right)}
- No
(x+3)cos⁡(x)=−(3−x)cos⁡(x)\left(x + 3\right) \cos{\left(x \right)} = - \left(3 - x\right) \cos{\left(x \right)}
- No
es decir, función
no es
par ni impar
Gráfico
Gráfico de la función y = y=(x+3)cosx
    © Sr Examen – Калькулятор