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(x-3)*cos(x)
Trazado el gráfico de la función/ (x-3)*cos(x)

Gráfico de la función y = (x-3)*cos(x)

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=32.9867228626928x_{1} = 32.9867228626928
x2=73.8274273593601x_{2} = 73.8274273593601
x3=4.71238898038469x_{3} = 4.71238898038469
x4=39.2699081698724x_{4} = 39.2699081698724
x5=95.8185759344887x_{5} = 95.8185759344887
x6=45.553093477052x_{6} = 45.553093477052
x7=70.6858347057703x_{7} = 70.6858347057703
x8=−10.9955742875643x_{8} = -10.9955742875643
x9=−58.1194640914112x_{9} = -58.1194640914112
x10=−23.5619449019235x_{10} = -23.5619449019235
x11=26.7035375555132x_{11} = 26.7035375555132
x12=−26.7035375555132x_{12} = -26.7035375555132
x13=−89.5353906273091x_{13} = -89.5353906273091
x14=−17.2787595947439x_{14} = -17.2787595947439
x15=−42.4115008234622x_{15} = -42.4115008234622
x16=−61.261056745001x_{16} = -61.261056745001
x17=92.6769832808989x_{17} = 92.6769832808989
x18=−76.9690200129499x_{18} = -76.9690200129499
x19=−92.6769832808989x_{19} = -92.6769832808989
x20=−98.9601685880785x_{20} = -98.9601685880785
x21=61.261056745001x_{21} = 61.261056745001
x22=−54.9778714378214x_{22} = -54.9778714378214
x23=42.4115008234622x_{23} = 42.4115008234622
x24=−64.4026493985908x_{24} = -64.4026493985908
x25=67.5442420521806x_{25} = 67.5442420521806
x26=−7.85398163397448x_{26} = -7.85398163397448
x27=80.1106126665397x_{27} = 80.1106126665397
x28=−14.1371669411541x_{28} = -14.1371669411541
x29=14.1371669411541x_{29} = 14.1371669411541
x30=−1.5707963267949x_{30} = -1.5707963267949
x31=1.5707963267949x_{31} = 1.5707963267949
x32=29.845130209103x_{32} = 29.845130209103
x33=10.9955742875643x_{33} = 10.9955742875643
x34=17.2787595947439x_{34} = 17.2787595947439
x35=−51.8362787842316x_{35} = -51.8362787842316
x36=3x_{36} = 3
x37=−29.845130209103x_{37} = -29.845130209103
x38=−48.6946861306418x_{38} = -48.6946861306418
x39=−73.8274273593601x_{39} = -73.8274273593601
x40=23.5619449019235x_{40} = 23.5619449019235
x41=20.4203522483337x_{41} = 20.4203522483337
x42=−86.3937979737193x_{42} = -86.3937979737193
x43=54.9778714378214x_{43} = 54.9778714378214
x44=58.1194640914112x_{44} = 58.1194640914112
x45=51.8362787842316x_{45} = 51.8362787842316
x46=−67.5442420521806x_{46} = -67.5442420521806
x47=−4.71238898038469x_{47} = -4.71238898038469
x48=−45.553093477052x_{48} = -45.553093477052
x49=−70.6858347057703x_{49} = -70.6858347057703
x50=48.6946861306418x_{50} = 48.6946861306418
x51=−83.2522053201295x_{51} = -83.2522053201295
x52=−95.8185759344887x_{52} = -95.8185759344887
x53=89.5353906273091x_{53} = 89.5353906273091
x54=−39.2699081698724x_{54} = -39.2699081698724
x55=76.9690200129499x_{55} = 76.9690200129499
x56=−32.9867228626928x_{56} = -32.9867228626928
x57=−20.4203522483337x_{57} = -20.4203522483337
x58=−36.1283155162826x_{58} = -36.1283155162826
x59=7.85398163397448x_{59} = 7.85398163397448
x60=−80.1106126665397x_{60} = -80.1106126665397
x61=86.3937979737193x_{61} = 86.3937979737193
x62=98.9601685880785x_{62} = 98.9601685880785
x63=36.1283155162826x_{63} = 36.1283155162826
x64=64.4026493985908x_{64} = 64.4026493985908
x65=83.2522053201295x_{65} = 83.2522053201295
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=72.2710660715932x_{1} = 72.2710660715932
x2=28.3138174685366x_{2} = 28.3138174685366
x3=−62.8470386162472x_{3} = -62.8470386162472
x4=−9.50457883886398x_{4} = -9.50457883886398
x5=−28.30626551274x_{5} = -28.30626551274
x6=2.22814103089124x_{6} = 2.22814103089124
x7=−65.9879399974437x_{7} = -65.9879399974437
x8=−78.5520778284944x_{8} = -78.5520778284944
x9=−50.2842475271843x_{9} = -50.2842475271843
x10=37.7278991803885x_{10} = 37.7278991803885
x11=31.4510601479335x_{11} = 31.4510601479335
x12=34.5891650451544x_{12} = 34.5891650451544
x13=78.5530512997373x_{13} = 78.5530512997373
x14=−97.3993321575476x_{14} = -97.3993321575476
x15=−56.5654544420077x_{15} = -56.5654544420077
x16=−75.4109763113185x_{16} = -75.4109763113185
x17=91.1175349460173x_{17} = 91.1175349460173
x18=−87.9755858178486x_{18} = -87.9755858178486
x19=−31.4449502153243x_{19} = -31.4449502153243
x20=3.95172192033919x_{20} = 3.95172192033919
x21=−91.1168116486103x_{21} = -91.1168116486103
x22=75.4120326678904x_{22} = 75.4120326678904
x23=69.130158920116x_{23} = 69.130158920116
x24=−81.6932157658594x_{24} = -81.6932157658594
x25=−22.0310776789363x_{25} = -22.0310776789363
x26=9.57569676385338x_{26} = 9.57569676385338
x27=47.1465377637573x_{27} = 47.1465377637573
x28=53.4269031964768x_{28} = 53.4269031964768
x29=−12.6302619891586x_{29} = -12.6302619891586
x30=−34.5841198954721x_{30} = -34.5841198954721
x31=−69.1289015588518x_{31} = -69.1289015588518
x32=40.8671065042713x_{32} = 40.8671065042713
x33=25.1778008415242x_{33} = 25.1778008415242
x34=94.2587370240534x_{34} = 94.2587370240534
x35=18.912317780113x_{35} = 18.912317780113
x36=−100.540622659664x_{36} = -100.540622659664
x37=44.0066785894522x_{37} = 44.0066785894522
x38=−3.29903328785148x_{38} = -3.29903328785148
x39=50.2866269338091x_{39} = 50.2866269338091
x40=−84.8343862178182x_{40} = -84.8343862178182
x41=−18.8951963232073x_{41} = -18.8951963232073
x42=100.541216632062x_{42} = 100.541216632062
x43=−0.294682454486773x_{43} = -0.294682454486773
x44=−40.8634985472455x_{44} = -40.8634985472455
x45=−72.2699157713744x_{45} = -72.2699157713744
x46=−47.1438297937958x_{46} = -47.1438297937958
x47=59.7078928202273x_{47} = 59.7078928202273
x48=−37.7236626573345x_{48} = -37.7236626573345
x49=97.3999650893223x_{49} = 97.3999650893223
x50=65.9893200989848x_{50} = 65.9893200989848
x51=56.567333690088x_{51} = 56.567333690088
x52=22.0436114382877x_{52} = 22.0436114382877
x53=−125.671477717255x_{53} = -125.671477717255
x54=15.786014834861x_{54} = 15.786014834861
x55=−94.2580611694573x_{55} = -94.2580611694573
x56=12.6694230459213x_{56} = 12.6694230459213
x57=87.9763617358531x_{57} = 87.9763617358531
x58=−44.0035689215071x_{58} = -44.0035689215071
x59=84.835220716198x_{59} = 84.835220716198
x60=−6.38928965648362x_{60} = -6.38928965648362
x61=−25.1682273173293x_{61} = -25.1682273173293
x62=62.8485603567807x_{62} = 62.8485603567807
x63=6.55723006500106x_{63} = 6.55723006500106
x64=−53.4247959606036x_{64} = -53.4247959606036
x65=−15.7612143304042x_{65} = -15.7612143304042
x66=−59.7062064512464x_{66} = -59.7062064512464
x67=81.6941157398245x_{67} = 81.6941157398245
Signos de extremos en los puntos:
(72.2710660715932, -69.2638491787087)

(28.31381746853661, -25.2940884985806)

(-62.84703861624724, -65.8394465735594)

(-9.504578838863976, 12.4647842585051)

(-28.30626551273998, 31.2903064803893)

(2.228141030891238, 0.471618974793956)

(-65.98793999744368, 68.9806934957898)

(-78.55207782849438, 81.545947468169)

(-50.28424752718431, -53.2748663689057)

(37.7278991803885, 34.7135104817292)

(31.45106014793351, 28.4335023766721)

(34.589165045154424, -31.5733487197023)

(78.55305129973732, -75.5464343027166)

(-97.39933215754765, 100.394352415252)

(-56.56545444200766, -59.5570620887982)

(-75.41097631131846, -78.4046004308088)

(91.11753494601734, -88.1118612545098)

(-87.97558581784861, -90.9700903358314)

(-31.444950215324322, -34.4304434690237)

(3.951721920339186, -0.656121661044172)

(-91.1168116486103, 94.1114995512231)

(75.41203266789043, 72.4051287256054)

(69.13015892011602, 66.1225993697551)

(-81.69321576585943, -84.6873127224841)

(-22.031077678936263, 25.0111263891723)

(9.575696763853385, -6.50095316217611)

(47.14653776375731, -44.1352162039481)

(53.42690319647679, -50.4169907777953)

(-12.63026198915859, -15.59837063305)

(-34.58411989547207, 37.5708234637983)

(-69.1289015588518, -72.121970523981)

(40.867106504271284, -37.8539093345704)

(25.177800841524213, 22.15529009427)

(94.25873702405337, 91.2532585899567)

(18.91231778011301, 15.8809883513863)

(-100.5406226596642, -103.535793974935)

(44.006678589452186, 40.9944908893309)

(-3.299033287851476, 6.22112560417095)

(50.28662693380906, 47.2760566650762)

(-84.83438621781819, 87.828694239774)

(-18.895196323207266, -21.8723959280207)

(100.54121663206242, 97.5360909979324)

(-0.2946824544867733, -3.15266324719375)

(-40.863498547245456, 43.8521039892383)

(-72.26991577137444, 75.2632738904155)

(-47.14382979379579, 50.1338614505173)

(59.707892820227336, -56.6990777612809)

(-37.72366265733454, -40.7113903330478)

(97.39996508932231, -94.3946689229274)

(65.98932009898483, -62.9813837455716)

(56.56733369008799, 53.558002082243)

(22.043611438287677, -19.0174100876084)

(-125.6714777172552, -128.667592028211)

(15.786014834860985, -12.7470881005591)

(-94.25806116945732, -97.2529206150062)

(12.669423045921281, 9.61812478108002)

(87.97636173585312, 84.9704783576549)

(-44.00356892150712, -46.9929350411195)

(84.83522071619804, -81.8291115616385)

(-6.389289656483623, -9.33648628773909)

(-25.168227317329272, -28.1504935824352)

(62.84856035678067, 59.840207685858)

(6.557230065001062, 3.42448900708588)

(-53.424795960603625, 56.4159366951519)

(-15.761214330404183, 18.7346202562976)

(-59.70620645124642, 62.6982342794497)

(81.69411573982451, 78.6877627940051)


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=72.2710660715932x_{1} = 72.2710660715932
x2=28.3138174685366x_{2} = 28.3138174685366
x3=−62.8470386162472x_{3} = -62.8470386162472
x4=−50.2842475271843x_{4} = -50.2842475271843
x5=34.5891650451544x_{5} = 34.5891650451544
x6=78.5530512997373x_{6} = 78.5530512997373
x7=−56.5654544420077x_{7} = -56.5654544420077
x8=−75.4109763113185x_{8} = -75.4109763113185
x9=91.1175349460173x_{9} = 91.1175349460173
x10=−87.9755858178486x_{10} = -87.9755858178486
x11=−31.4449502153243x_{11} = -31.4449502153243
x12=3.95172192033919x_{12} = 3.95172192033919
x13=−81.6932157658594x_{13} = -81.6932157658594
x14=9.57569676385338x_{14} = 9.57569676385338
x15=47.1465377637573x_{15} = 47.1465377637573
x16=53.4269031964768x_{16} = 53.4269031964768
x17=−12.6302619891586x_{17} = -12.6302619891586
x18=−69.1289015588518x_{18} = -69.1289015588518
x19=40.8671065042713x_{19} = 40.8671065042713
x20=−100.540622659664x_{20} = -100.540622659664
x21=−18.8951963232073x_{21} = -18.8951963232073
x22=−0.294682454486773x_{22} = -0.294682454486773
x23=59.7078928202273x_{23} = 59.7078928202273
x24=−37.7236626573345x_{24} = -37.7236626573345
x25=97.3999650893223x_{25} = 97.3999650893223
x26=65.9893200989848x_{26} = 65.9893200989848
x27=22.0436114382877x_{27} = 22.0436114382877
x28=−125.671477717255x_{28} = -125.671477717255
x29=15.786014834861x_{29} = 15.786014834861
x30=−94.2580611694573x_{30} = -94.2580611694573
x31=−44.0035689215071x_{31} = -44.0035689215071
x32=84.835220716198x_{32} = 84.835220716198
x33=−6.38928965648362x_{33} = -6.38928965648362
x34=−25.1682273173293x_{34} = -25.1682273173293
Puntos máximos de la función:
x34=−9.50457883886398x_{34} = -9.50457883886398
x34=−28.30626551274x_{34} = -28.30626551274
x34=2.22814103089124x_{34} = 2.22814103089124
x34=−65.9879399974437x_{34} = -65.9879399974437
x34=−78.5520778284944x_{34} = -78.5520778284944
x34=37.7278991803885x_{34} = 37.7278991803885
x34=31.4510601479335x_{34} = 31.4510601479335
x34=−97.3993321575476x_{34} = -97.3993321575476
x34=−91.1168116486103x_{34} = -91.1168116486103
x34=75.4120326678904x_{34} = 75.4120326678904
x34=69.130158920116x_{34} = 69.130158920116
x34=−22.0310776789363x_{34} = -22.0310776789363
x34=−34.5841198954721x_{34} = -34.5841198954721
x34=25.1778008415242x_{34} = 25.1778008415242
x34=94.2587370240534x_{34} = 94.2587370240534
x34=18.912317780113x_{34} = 18.912317780113
x34=44.0066785894522x_{34} = 44.0066785894522
x34=−3.29903328785148x_{34} = -3.29903328785148
x34=50.2866269338091x_{34} = 50.2866269338091
x34=−84.8343862178182x_{34} = -84.8343862178182
x34=100.541216632062x_{34} = 100.541216632062
x34=−40.8634985472455x_{34} = -40.8634985472455
x34=−72.2699157713744x_{34} = -72.2699157713744
x34=−47.1438297937958x_{34} = -47.1438297937958
x34=56.567333690088x_{34} = 56.567333690088
x34=12.6694230459213x_{34} = 12.6694230459213
x34=87.9763617358531x_{34} = 87.9763617358531
x34=62.8485603567807x_{34} = 62.8485603567807
x34=6.55723006500106x_{34} = 6.55723006500106
x34=−53.4247959606036x_{34} = -53.4247959606036
x34=−15.7612143304042x_{34} = -15.7612143304042
x34=−59.7062064512464x_{34} = -59.7062064512464
x34=81.6941157398245x_{34} = 81.6941157398245
Decrece en los intervalos
[97.3999650893223,∞)\left[97.3999650893223, \infty\right)
Crece en los intervalos
(−∞,−125.671477717255]\left(-\infty, -125.671477717255\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=48.7383852414105x_{2} = 48.7383852414105
x3=61.2953513467577x_{3} = 61.2953513467577
x4=−33.0421565872763x_{4} = -33.0421565872763
x5=−26.770617096282x_{5} = -26.770617096282
x6=5.40591660043711x_{6} = 5.40591660043711
x7=58.1557091900213x_{7} = 58.1557091900213
x8=−14.2525765162628x_{8} = -14.2525765162628
x9=64.4351925360079x_{9} = 64.4351925360079
x10=83.2771138683158x_{10} = 83.2771138683158
x11=45.6000073775805x_{11} = 45.6000073775805
x12=−67.5725740899573x_{12} = -67.5725740899573
x13=3.09441845244876x_{13} = 3.09441845244876
x14=−48.7333266866217x_{14} = -48.7333266866217
x15=−20.5052352226731x_{15} = -20.5052352226731
x16=33.053173593001x_{16} = 33.053173593001
x17=26.7874183328987x_{17} = 26.7874183328987
x18=42.462138986437x_{18} = 42.462138986437
x19=70.7153615177027x_{19} = 70.7153615177027
x20=−76.9940166753296x_{20} = -76.9940166753296
x21=0.826862867228188x_{21} = 0.826862867228188
x22=−39.3171352054588x_{22} = -39.3171352054588
x23=29.9192901213547x_{23} = 29.9192901213547
x24=−45.5942274137072x_{24} = -45.5942274137072
x25=−1.95446769860329x_{25} = -1.95446769860329
x26=80.1365349095748x_{26} = 80.1365349095748
x27=−95.8388081401923x_{27} = -95.8388081401923
x28=−73.8534450440396x_{28} = -73.8534450440396
x29=98.9810030297478x_{29} = 98.9810030297478
x30=−83.2753827526075x_{30} = -83.2753827526075
x31=−80.1346653801375x_{31} = -80.1346653801375
x32=−58.1521577434381x_{32} = -58.1521577434381
x33=39.3249112691049x_{33} = 39.3249112691049
x34=−70.7129603215986x_{34} = -70.7129603215986
x35=−64.432300083121x_{35} = -64.432300083121
x36=−36.1793185853157x_{36} = -36.1793185853157
x37=23.6584567792085x_{37} = 23.6584567792085
x38=76.996041906774x_{38} = 76.996041906774
x39=55.0163019917346x_{39} = 55.0163019917346
x40=36.1885045575189x_{40} = 36.1885045575189
x41=20.5339259723255x_{41} = 20.5339259723255
x42=67.5752037953155x_{42} = 67.5752037953155
x43=−55.0123332166132x_{43} = -55.0123332166132
x44=−98.9797778056003x_{44} = -98.9797778056003
x45=17.4166086363428x_{45} = 17.4166086363428
x46=95.8401150148972x_{46} = 95.8401150148972
x47=89.5584922796575x_{47} = 89.5584922796575
x48=−42.4554715670068x_{48} = -42.4554715670068
x49=−92.6978793436777x_{49} = -92.6978793436777
x50=−23.6368881258944x_{50} = -23.6368881258944
x51=86.4177690883985x_{51} = 86.4177690883985
x52=−4.9585915020369x_{52} = -4.9585915020369
x53=−89.5569955724082x_{53} = -89.5569955724082
x54=−61.2921547109207x_{54} = -61.2921547109207
x55=8.21987886514604x_{55} = 8.21987886514604
x56=73.8556462692966x_{56} = 73.8556462692966
x57=−11.136122961567x_{57} = -11.136122961567
x58=−86.4161615658675x_{58} = -86.4161615658675
x59=−29.9058350256858x_{59} = -29.9058350256858
x60=51.8771748648305x_{60} = 51.8771748648305
x61=−17.3765980243604x_{61} = -17.3765980243604
x62=11.2338590161227x_{62} = 11.2338590161227
x63=92.6992763110302x_{63} = 92.6992763110302
x64=−51.8727106470714x_{64} = -51.8727106470714
x65=−8.03330382965524x_{65} = -8.03330382965524

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
[95.8401150148972,∞)\left[95.8401150148972, \infty\right)
Convexa en los intervalos
(−∞,−95.8388081401923]\left(-\infty, -95.8388081401923\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)=(−x−3)cos⁡(x)\left(x - 3\right) \cos{\left(x \right)} = \left(- x - 3\right) \cos{\left(x \right)}
- No
(x−3)cos⁡(x)=−(−x−3)cos⁡(x)\left(x - 3\right) \cos{\left(x \right)} = - \left(- x - 3\right) \cos{\left(x \right)}
- No
es decir, función
no es
par ni impar
Gráfico
Gráfico de la función y = (x-3)*cos(x)
    © Sr Examen – Калькулятор