Mister Exam

Other calculators

  • How to use it?

  • Graphing y =:
  • x^3+4x-7
  • x^3+6*x^2+9*x
  • x^2+6x+8
  • x^2-2x+8
  • Derivative of:
  • x^3*cos(x) x^3*cos(x)
  • Limit of the function:
  • x^3*cos(x) x^3*cos(x)
  • Integral of d{x}:
  • x^3*cos(x)

  • Identical expressions

  • x^ three *cos(x)
  • x cubed multiply by co sinus of e of (x)
  • x to the power of three multiply by co sinus of e of (x)
  • x3*cos(x)
  • x3*cosx
  • x³*cos(x)
  • x to the power of 3*cos(x)
  • x^3cos(x)
  • x3cos(x)
  • x3cosx
  • x^3cosx

  • Similar expressions

  • x^3*cosx
Plotting a function graph/ x^3*cos(x)

Graphing y = x^3*cos(x)

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
        3       
f(x) = x *cos(x)
f(x)=x3cos⁡(x)f{\left(x \right)} = x^{3} \cos{\left(x \right)} 
f = x^3*cos(x)
The graph of the function
012345678-2-1-500500
The points of intersection with the X-axis coordinate
Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
x3cos⁡(x)=0x^{3} \cos{\left(x \right)} = 0
Solve this equation
The points of intersection with the axis X:

Analytical solution
x1=0x_{1} = 0
x2=−π2x_{2} = - \frac{\pi}{2}
x3=π2x_{3} = \frac{\pi}{2}
Numerical solution
x1=4.71238898038469x_{1} = 4.71238898038469
x2=17.2787595947439x_{2} = 17.2787595947439
x3=−89.5353906273091x_{3} = -89.5353906273091
x4=64.4026493985908x_{4} = 64.4026493985908
x5=70.6858347057703x_{5} = 70.6858347057703
x6=36.1283155162826x_{6} = 36.1283155162826
x7=−98.9601685880785x_{7} = -98.9601685880785
x8=48.6946861306418x_{8} = 48.6946861306418
x9=−58.1194640914112x_{9} = -58.1194640914112
x10=7.85398163397448x_{10} = 7.85398163397448
x11=39.2699081698724x_{11} = 39.2699081698724
x12=−95.8185759344887x_{12} = -95.8185759344887
x13=−1.5707963267949x_{13} = -1.5707963267949
x14=−92.6769832808989x_{14} = -92.6769832808989
x15=−23.5619449019235x_{15} = -23.5619449019235
x16=23.5619449019235x_{16} = 23.5619449019235
x17=61.261056745001x_{17} = 61.261056745001
x18=29.845130209103x_{18} = 29.845130209103
x19=−32.9867228626928x_{19} = -32.9867228626928
x20=−51.8362787842316x_{20} = -51.8362787842316
x21=−80.1106126665397x_{21} = -80.1106126665397
x22=−83.2522053201295x_{22} = -83.2522053201295
x23=67.5442420521806x_{23} = 67.5442420521806
x24=98.9601685880785x_{24} = 98.9601685880785
x25=92.6769832808989x_{25} = 92.6769832808989
x26=−39.2699081698724x_{26} = -39.2699081698724
x27=86.3937979737193x_{27} = 86.3937979737193
x28=45.553093477052x_{28} = 45.553093477052
x29=−67.5442420521806x_{29} = -67.5442420521806
x30=51.8362787842316x_{30} = 51.8362787842316
x31=76.9690200129499x_{31} = 76.9690200129499
x32=−26.7035375555132x_{32} = -26.7035375555132
x33=−4.71238898038469x_{33} = -4.71238898038469
x34=95.8185759344887x_{34} = 95.8185759344887
x35=−86.3937979737193x_{35} = -86.3937979737193
x36=−10.9955742875643x_{36} = -10.9955742875643
x37=83.2522053201295x_{37} = 83.2522053201295
x38=−7.85398163397448x_{38} = -7.85398163397448
x39=−36.1283155162826x_{39} = -36.1283155162826
x40=−17.2787595947439x_{40} = -17.2787595947439
x41=−14.1371669411541x_{41} = -14.1371669411541
x42=20.4203522483337x_{42} = 20.4203522483337
x43=54.9778714378214x_{43} = 54.9778714378214
x44=−70.6858347057703x_{44} = -70.6858347057703
x45=−48.6946861306418x_{45} = -48.6946861306418
x46=−54.9778714378214x_{46} = -54.9778714378214
x47=−45.553093477052x_{47} = -45.553093477052
x48=14.1371669411541x_{48} = 14.1371669411541
x49=−73.8274273593601x_{49} = -73.8274273593601
x50=26.7035375555132x_{50} = 26.7035375555132
x51=89.5353906273091x_{51} = 89.5353906273091
x52=10.9955742875643x_{52} = 10.9955742875643
x53=80.1106126665397x_{53} = 80.1106126665397
x54=73.8274273593601x_{54} = 73.8274273593601
x55=58.1194640914112x_{55} = 58.1194640914112
x56=−61.261056745001x_{56} = -61.261056745001
x57=1.5707963267949x_{57} = 1.5707963267949
x58=−20.4203522483337x_{58} = -20.4203522483337
x59=−42.4115008234622x_{59} = -42.4115008234622
x60=32.9867228626928x_{60} = 32.9867228626928
x61=0x_{61} = 0
x62=42.4115008234622x_{62} = 42.4115008234622
x63=−76.9690200129499x_{63} = -76.9690200129499
x64=−64.4026493985908x_{64} = -64.4026493985908
x65=−29.845130209103x_{65} = -29.845130209103
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to x^3*cos(x).
03cos⁡(0)0^{3} \cos{\left(0 \right)}
The result:
f(0)=0f{\left(0 \right)} = 0
The point:
(0, 0)
Extrema of the function
In order to find the extrema, we need to solve the equation
ddxf(x)=0\frac{d}{d x} f{\left(x \right)} = 0
(the derivative equals zero),
and the roots of this equation are the extrema of this function:
ddxf(x)=\frac{d}{d x} f{\left(x \right)} =
the first derivative
−x3sin⁡(x)+3x2cos⁡(x)=0- x^{3} \sin{\left(x \right)} + 3 x^{2} \cos{\left(x \right)} = 0
Solve this equation
The roots of this equation
x1=−87.9986725257711x_{1} = -87.9986725257711
x2=31.510845756676x_{2} = 31.510845756676
x3=−28.3796522911214x_{3} = -28.3796522911214
x4=−75.4379705139506x_{4} = -75.4379705139506
x5=−100.560788770886x_{5} = -100.560788770886
x6=0x_{6} = 0
x7=−22.12591435735x_{7} = -22.12591435735
x8=−34.6438990396267x_{8} = -34.6438990396267
x9=−84.8583399660622x_{9} = -84.8583399660622
x10=62.8795272030449x_{10} = 62.8795272030449
x11=28.3796522911214x_{11} = 28.3796522911214
x12=−94.2795891235637x_{12} = -94.2795891235637
x13=−66.0188560490172x_{13} = -66.0188560490172
x14=−59.7404355133729x_{14} = -59.7404355133729
x15=−25.2509941253717x_{15} = -25.2509941253717
x16=−56.6016202331048x_{16} = -56.6016202331048
x17=−3.80876221919969x_{17} = -3.80876221919969
x18=−78.5779764426249x_{18} = -78.5779764426249
x19=78.5779764426249x_{19} = 78.5779764426249
x20=72.2981021067071x_{20} = 72.2981021067071
x21=91.1390917936668x_{21} = 91.1390917936668
x22=12.7966483902814x_{22} = 12.7966483902814
x23=−62.8795272030449x_{23} = -62.8795272030449
x24=47.1873806732917x_{24} = 47.1873806732917
x25=15.8945130636842x_{25} = 15.8945130636842
x26=53.4631297645908x_{26} = 53.4631297645908
x27=−53.4631297645908x_{27} = -53.4631297645908
x28=−1.19245882933643x_{28} = -1.19245882933643
x29=56.6016202331048x_{29} = 56.6016202331048
x30=−40.913898225293x_{30} = -40.913898225293
x31=−47.1873806732917x_{31} = -47.1873806732917
x32=19.0061082873963x_{32} = 19.0061082873963
x33=50.325024483292x_{33} = 50.325024483292
x34=75.4379705139506x_{34} = 75.4379705139506
x35=40.913898225293x_{35} = 40.913898225293
x36=84.8583399660622x_{36} = 84.8583399660622
x37=9.72402747617551x_{37} = 9.72402747617551
x38=−69.1583898858035x_{38} = -69.1583898858035
x39=−15.8945130636842x_{39} = -15.8945130636842
x40=66.0188560490172x_{40} = 66.0188560490172
x41=−72.2981021067071x_{41} = -72.2981021067071
x42=−81.7181040853573x_{42} = -81.7181040853573
x43=34.6438990396267x_{43} = 34.6438990396267
x44=−44.0502961191214x_{44} = -44.0502961191214
x45=−97.4201569811411x_{45} = -97.4201569811411
x46=25.2509941253717x_{46} = 25.2509941253717
x47=6.70395577578075x_{47} = 6.70395577578075
x48=−37.7783560989567x_{48} = -37.7783560989567
x49=−12.7966483902814x_{49} = -12.7966483902814
x50=94.2795891235637x_{50} = 94.2795891235637
x51=−9.72402747617551x_{51} = -9.72402747617551
x52=1.19245882933643x_{52} = 1.19245882933643
x53=−6.70395577578075x_{53} = -6.70395577578075
x54=69.1583898858035x_{54} = 69.1583898858035
x55=−50.325024483292x_{55} = -50.325024483292
x56=44.0502961191214x_{56} = 44.0502961191214
x57=97.4201569811411x_{57} = 97.4201569811411
x58=37.7783560989567x_{58} = 37.7783560989567
x59=87.9986725257711x_{59} = 87.9986725257711
x60=100.560788770886x_{60} = 100.560788770886
x61=−31.510845756676x_{61} = -31.510845756676
x62=3.80876221919969x_{62} = 3.80876221919969
x63=81.7181040853573x_{63} = 81.7181040853573
x64=−19.0061082873963x_{64} = -19.0061082873963
x65=59.7404355133729x_{65} = 59.7404355133729
x66=−91.1390917936668x_{66} = -91.1390917936668
x67=22.12591435735x_{67} = 22.12591435735
The values of the extrema at the points:
(-87.99867252577111, -681045.511399255)

(31.51084575667604, 31147.3291476214)

(-28.37965229112142, 22730.4563261038)

(-75.43797051395065, -428969.926773577)

(-100.56078877088648, -1016465.96298217)

(0, 0)

(-22.125914357349984, 10733.6615463961)

(-34.64389903962671, 41424.5724319187)

(-84.85833996606219, 610678.128197996)

(62.87952720304487, 248332.79602616)

(28.37965229112142, -22730.4563261038)

(-94.27958912356374, -837593.47806229)

(-66.01885604901719, 287445.855707585)

(-59.74043551337287, 212940.488750329)

(-25.25099412537165, -15987.9141234403)

(-56.60162023310481, -181082.896088805)

(-3.808762219199689, 43.4050129540828)

(-78.57797644262494, 484826.373587257)

(78.57797644262494, -484826.373587257)

(72.29810210670713, -377578.383339478)

(91.13909179366682, -756621.948790976)

(12.796648390281426, 2040.19006584704)

(-62.87952720304487, -248332.79602616)

(47.18738067329166, -104858.027361626)

(15.894513063684203, -3945.84968737938)

(53.463129764590846, -152573.980219896)

(-53.463129764590846, 152573.980219896)

(-1.1924588293364287, -0.626323798219316)

(56.60162023310481, 181082.896088805)

(-40.91389822529297, 68304.326534245)

(-47.18738067329166, 104858.027361626)

(19.006108287396344, 6781.65561120486)

(50.32502448329199, 127227.703282192)

(75.43797051395065, 428969.926773577)

(40.91389822529297, -68304.326534245)

(84.85833996606219, -610678.128197996)

(9.72402747617551, -878.608875900237)

(-69.15838988580347, -330465.705562301)

(-15.894513063684203, 3945.84968737938)

(66.01885604901719, -287445.855707585)

(-72.29810210670713, 377578.383339478)

(-81.71810408535728, -545333.761493627)

(34.64389903962671, -41424.5724319187)

(-44.05029611912139, -85278.9144731517)

(-97.42015698114113, 924146.136898602)

(25.25099412537165, 15987.9141234403)

(6.703955775780748, 275.015342086354)

(-37.77835609895673, -53748.2253256845)

(-12.796648390281426, -2040.19006584704)

(94.27958912356374, 837593.47806229)

(-9.72402747617551, 878.608875900237)

(1.1924588293364287, 0.626323798219316)

(-6.703955775780748, -275.015342086354)

(69.15838988580347, 330465.705562301)

(-50.32502448329199, -127227.703282192)

(44.05029611912139, 85278.9144731517)

(97.42015698114113, -924146.136898602)

(37.77835609895673, 53748.2253256845)

(87.99867252577111, 681045.511399255)

(100.56078877088648, 1016465.96298217)

(-31.51084575667604, -31147.3291476214)

(3.808762219199689, -43.4050129540828)

(81.71810408535728, 545333.761493627)

(-19.006108287396344, -6781.65561120486)

(59.74043551337287, -212940.488750329)

(-91.13909179366682, 756621.948790976)

(22.125914357349984, -10733.6615463961)


Intervals of increase and decrease of the function:
Let's find intervals where the function increases and decreases, as well as minima and maxima of the function, for this let's look how the function behaves itself in the extremas and at the slightest deviation from:
Minima of the function at points:
x1=−87.9986725257711x_{1} = -87.9986725257711
x2=−75.4379705139506x_{2} = -75.4379705139506
x3=−100.560788770886x_{3} = -100.560788770886
x4=28.3796522911214x_{4} = 28.3796522911214
x5=−94.2795891235637x_{5} = -94.2795891235637
x6=−25.2509941253717x_{6} = -25.2509941253717
x7=−56.6016202331048x_{7} = -56.6016202331048
x8=78.5779764426249x_{8} = 78.5779764426249
x9=72.2981021067071x_{9} = 72.2981021067071
x10=91.1390917936668x_{10} = 91.1390917936668
x11=−62.8795272030449x_{11} = -62.8795272030449
x12=47.1873806732917x_{12} = 47.1873806732917
x13=15.8945130636842x_{13} = 15.8945130636842
x14=53.4631297645908x_{14} = 53.4631297645908
x15=−1.19245882933643x_{15} = -1.19245882933643
x16=40.913898225293x_{16} = 40.913898225293
x17=84.8583399660622x_{17} = 84.8583399660622
x18=9.72402747617551x_{18} = 9.72402747617551
x19=−69.1583898858035x_{19} = -69.1583898858035
x20=66.0188560490172x_{20} = 66.0188560490172
x21=−81.7181040853573x_{21} = -81.7181040853573
x22=34.6438990396267x_{22} = 34.6438990396267
x23=−44.0502961191214x_{23} = -44.0502961191214
x24=−37.7783560989567x_{24} = -37.7783560989567
x25=−12.7966483902814x_{25} = -12.7966483902814
x26=−6.70395577578075x_{26} = -6.70395577578075
x27=−50.325024483292x_{27} = -50.325024483292
x28=97.4201569811411x_{28} = 97.4201569811411
x29=−31.510845756676x_{29} = -31.510845756676
x30=3.80876221919969x_{30} = 3.80876221919969
x31=−19.0061082873963x_{31} = -19.0061082873963
x32=59.7404355133729x_{32} = 59.7404355133729
x33=22.12591435735x_{33} = 22.12591435735
Maxima of the function at points:
x33=31.510845756676x_{33} = 31.510845756676
x33=−28.3796522911214x_{33} = -28.3796522911214
x33=−22.12591435735x_{33} = -22.12591435735
x33=−34.6438990396267x_{33} = -34.6438990396267
x33=−84.8583399660622x_{33} = -84.8583399660622
x33=62.8795272030449x_{33} = 62.8795272030449
x33=−66.0188560490172x_{33} = -66.0188560490172
x33=−59.7404355133729x_{33} = -59.7404355133729
x33=−3.80876221919969x_{33} = -3.80876221919969
x33=−78.5779764426249x_{33} = -78.5779764426249
x33=12.7966483902814x_{33} = 12.7966483902814
x33=−53.4631297645908x_{33} = -53.4631297645908
x33=56.6016202331048x_{33} = 56.6016202331048
x33=−40.913898225293x_{33} = -40.913898225293
x33=−47.1873806732917x_{33} = -47.1873806732917
x33=19.0061082873963x_{33} = 19.0061082873963
x33=50.325024483292x_{33} = 50.325024483292
x33=75.4379705139506x_{33} = 75.4379705139506
x33=−15.8945130636842x_{33} = -15.8945130636842
x33=−72.2981021067071x_{33} = -72.2981021067071
x33=−97.4201569811411x_{33} = -97.4201569811411
x33=25.2509941253717x_{33} = 25.2509941253717
x33=6.70395577578075x_{33} = 6.70395577578075
x33=94.2795891235637x_{33} = 94.2795891235637
x33=−9.72402747617551x_{33} = -9.72402747617551
x33=1.19245882933643x_{33} = 1.19245882933643
x33=69.1583898858035x_{33} = 69.1583898858035
x33=44.0502961191214x_{33} = 44.0502961191214
x33=37.7783560989567x_{33} = 37.7783560989567
x33=87.9986725257711x_{33} = 87.9986725257711
x33=100.560788770886x_{33} = 100.560788770886
x33=81.7181040853573x_{33} = 81.7181040853573
x33=−91.1390917936668x_{33} = -91.1390917936668
Decreasing at intervals
[97.4201569811411,∞)\left[97.4201569811411, \infty\right)
Increasing at intervals
(−∞,−100.560788770886]\left(-\infty, -100.560788770886\right]
Inflection points
Let's find the inflection points, we'll need to solve the equation for this
d2dx2f(x)=0\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0
(the second derivative equals zero),
the roots of this equation will be the inflection points for the specified function graph:
d2dx2f(x)=\frac{d^{2}}{d x^{2}} f{\left(x \right)} =
the second derivative
x(−x2cos⁡(x)−6xsin⁡(x)+6cos⁡(x))=0x \left(- x^{2} \cos{\left(x \right)} - 6 x \sin{\left(x \right)} + 6 \cos{\left(x \right)}\right) = 0
Solve this equation
The roots of this equation
x1=80.185369601293x_{1} = 80.185369601293
x2=−99.0207249350603x_{2} = -99.0207249350603
x3=39.4215265901233x_{3} = 39.4215265901233
x4=−64.495545315785x_{4} = -64.495545315785
x5=−61.3586871153543x_{5} = -61.3586871153543
x6=−39.4215265901233x_{6} = -39.4215265901233
x7=0x_{7} = 0
x8=14.538821316956x_{8} = 14.538821316956
x9=17.6130932998928x_{9} = 17.6130932998928
x10=73.9085198432299x_{10} = 73.9085198432299
x11=−8.50941039706366x_{11} = -8.50941039706366
x12=−73.9085198432299x_{12} = -73.9085198432299
x13=26.924570790473x_{13} = 26.924570790473
x14=45.6840551197015x_{14} = 45.6840551197015
x15=5.63254352434708x_{15} = 5.63254352434708
x16=95.8811126479692x_{16} = 95.8811126479692
x17=−0.822926400561141x_{17} = -0.822926400561141
x18=−23.811319714972x_{18} = -23.811319714972
x19=−77.0468162058446x_{19} = -77.0468162058446
x20=58.2223356290493x_{20} = 58.2223356290493
x21=36.2928915290304x_{21} = 36.2928915290304
x22=30.0435319479484x_{22} = 30.0435319479484
x23=20.7061859967519x_{23} = 20.7061859967519
x24=−92.741634081119x_{24} = -92.741634081119
x25=−33.1666524059798x_{25} = -33.1666524059798
x26=−5.63254352434708x_{26} = -5.63254352434708
x27=−58.2223356290493x_{27} = -58.2223356290493
x28=−17.6130932998928x_{28} = -17.6130932998928
x29=23.811319714972x_{29} = 23.811319714972
x30=−95.8811126479692x_{30} = -95.8811126479692
x31=−42.5520407715344x_{31} = -42.5520407715344
x32=−51.9515155836453x_{32} = -51.9515155836453
x33=−80.185369601293x_{33} = -80.185369601293
x34=8.50941039706366x_{34} = 8.50941039706366
x35=−36.2928915290304x_{35} = -36.2928915290304
x36=−55.0865764667238x_{36} = -55.0865764667238
x37=64.495545315785x_{37} = 64.495545315785
x38=33.1666524059798x_{38} = 33.1666524059798
x39=−2.98146897551057x_{39} = -2.98146897551057
x40=67.6328403186065x_{40} = 67.6328403186065
x41=89.6023032306285x_{41} = 89.6023032306285
x42=86.4631361132255x_{42} = 86.4631361132255
x43=51.9515155836453x_{43} = 51.9515155836453
x44=99.0207249350603x_{44} = 99.0207249350603
x45=61.3586871153543x_{45} = 61.3586871153543
x46=−26.924570790473x_{46} = -26.924570790473
x47=−83.3241511438861x_{47} = -83.3241511438861
x48=−48.8172856736618x_{48} = -48.8172856736618
x49=77.0468162058446x_{49} = 77.0468162058446
x50=102.160458658341x_{50} = 102.160458658341
x51=92.741634081119x_{51} = 92.741634081119
x52=55.0865764667238x_{52} = 55.0865764667238
x53=48.8172856736618x_{53} = 48.8172856736618
x54=−45.6840551197015x_{54} = -45.6840551197015
x55=−11.495916748171x_{55} = -11.495916748171
x56=−86.4631361132255x_{56} = -86.4631361132255
x57=−89.6023032306285x_{57} = -89.6023032306285
x58=2.98146897551057x_{58} = 2.98146897551057
x59=−70.7705144780994x_{59} = -70.7705144780994
x60=42.5520407715344x_{60} = 42.5520407715344
x61=−14.538821316956x_{61} = -14.538821316956
x62=−30.0435319479484x_{62} = -30.0435319479484
x63=70.7705144780994x_{63} = 70.7705144780994
x64=−67.6328403186065x_{64} = -67.6328403186065
x65=−20.7061859967519x_{65} = -20.7061859967519
x66=83.3241511438861x_{66} = 83.3241511438861
x67=11.495916748171x_{67} = 11.495916748171

Сonvexity and concavity intervals:
Let’s find the intervals where the function is convex or concave, for this look at the behaviour of the function at the inflection points:
Concave at the intervals
[102.160458658341,∞)\left[102.160458658341, \infty\right)
Convex at the intervals
(−∞,−95.8811126479692]\left(-\infty, -95.8811126479692\right]
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
lim⁡x→−∞(x3cos⁡(x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(x^{3} \cos{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle
Let's take the limit
so,
equation of the horizontal asymptote on the left:
y=⟨−∞,∞⟩y = \left\langle -\infty, \infty\right\rangle
lim⁡x→∞(x3cos⁡(x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(x^{3} \cos{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle
Let's take the limit
so,
equation of the horizontal asymptote on the right:
y=⟨−∞,∞⟩y = \left\langle -\infty, \infty\right\rangle
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of x^3*cos(x), divided by x at x->+oo and x ->-oo
lim⁡x→−∞(x2cos⁡(x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(x^{2} \cos{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle
Let's take the limit
so,
inclined asymptote equation on the left:
y=⟨−∞,∞⟩xy = \left\langle -\infty, \infty\right\rangle x
lim⁡x→∞(x2cos⁡(x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(x^{2} \cos{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle
Let's take the limit
so,
inclined asymptote equation on the right:
y=⟨−∞,∞⟩xy = \left\langle -\infty, \infty\right\rangle x
Even and odd functions
Let's check, whether the function even or odd by using relations f = f(-x) и f = -f(-x).
So, check:
x3cos⁡(x)=−x3cos⁡(x)x^{3} \cos{\left(x \right)} = - x^{3} \cos{\left(x \right)}
- No
x3cos⁡(x)=x3cos⁡(x)x^{3} \cos{\left(x \right)} = x^{3} \cos{\left(x \right)}
- Yes
so, the function
is
odd
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