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xcosx+x^2sinx
Plotting a function graph/ xcosx+x^2sinx

Graphing y = xcosx+x^2sinx

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

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                   2       
f(x) = x*cos(x) + x *sin(x)
f(x)=x2sin⁡(x)+xcos⁡(x)f{\left(x \right)} = x^{2} \sin{\left(x \right)} + x \cos{\left(x \right)} 
f = x^2*sin(x) + x*cos(x)
The graph of the function
0-100-80-60-40-2020406080100-100100
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:
x2sin⁡(x)+xcos⁡(x)=0x^{2} \sin{\left(x \right)} + x \cos{\left(x \right)} = 0
Solve this equation
The points of intersection with the axis X:

Numerical solution
x1=−18.7964043662102x_{1} = -18.7964043662102
x2=100.521017074687x_{2} = 100.521017074687
x3=−100.521017074687x_{3} = -100.521017074687
x4=40.8162093266346x_{4} = 40.8162093266346
x5=−87.9532251106725x_{5} = -87.9532251106725
x6=62.8159348889734x_{6} = 62.8159348889734
x7=−9.31786646179107x_{7} = -9.31786646179107
x8=−97.3791034786112x_{8} = -97.3791034786112
x9=34.5285657554621x_{9} = 34.5285657554621
x10=43.9595528888955x_{10} = 43.9595528888955
x11=72.2427897046973x_{11} = 72.2427897046973
x12=−43.9595528888955x_{12} = -43.9595528888955
x13=6.12125046689807x_{13} = 6.12125046689807
x14=−65.9582857893902x_{14} = -65.9582857893902
x15=65.9582857893902x_{15} = 65.9582857893902
x16=−84.811211299318x_{16} = -84.811211299318
x17=2.79838604578389x_{17} = 2.79838604578389
x18=−28.2389365752603x_{18} = -28.2389365752603
x19=91.0952098694071x_{19} = 91.0952098694071
x20=69.100567727981x_{20} = 69.100567727981
x21=56.5309801938186x_{21} = 56.5309801938186
x22=18.7964043662102x_{22} = 18.7964043662102
x23=97.3791034786112x_{23} = 97.3791034786112
x24=50.2455828375744x_{24} = 50.2455828375744
x25=47.1026627703624x_{25} = 47.1026627703624
x26=9.31786646179107x_{26} = 9.31786646179107
x27=−40.8162093266346x_{27} = -40.8162093266346
x28=59.6735041304405x_{28} = 59.6735041304405
x29=−53.3883466217256x_{29} = -53.3883466217256
x30=−15.644128370333x_{30} = -15.644128370333
x31=−37.672573565113x_{31} = -37.672573565113
x32=37.672573565113x_{32} = 37.672573565113
x33=31.3840740178899x_{33} = 31.3840740178899
x34=−75.3849592185347x_{34} = -75.3849592185347
x35=−62.8159348889734x_{35} = -62.8159348889734
x36=15.644128370333x_{36} = 15.644128370333
x37=25.0929104121121x_{37} = 25.0929104121121
x38=−50.2455828375744x_{38} = -50.2455828375744
x39=−12.4864543952238x_{39} = -12.4864543952238
x40=−31.3840740178899x_{40} = -31.3840740178899
x41=0x_{41} = 0
x42=−21.945612879981x_{42} = -21.945612879981
x43=−91.0952098694071x_{43} = -91.0952098694071
x44=84.811211299318x_{44} = 84.811211299318
x45=−69.100567727981x_{45} = -69.100567727981
x46=−25.0929104121121x_{46} = -25.0929104121121
x47=87.9532251106725x_{47} = 87.9532251106725
x48=12.4864543952238x_{48} = 12.4864543952238
x49=−56.5309801938186x_{49} = -56.5309801938186
x50=−78.5270825679419x_{50} = -78.5270825679419
x51=−59.6735041304405x_{51} = -59.6735041304405
x52=75.3849592185347x_{52} = 75.3849592185347
x53=28.2389365752603x_{53} = 28.2389365752603
x54=53.3883466217256x_{54} = 53.3883466217256
x55=78.5270825679419x_{55} = 78.5270825679419
x56=−47.1026627703624x_{56} = -47.1026627703624
x57=−72.2427897046973x_{57} = -72.2427897046973
x58=−34.5285657554621x_{58} = -34.5285657554621
x59=−94.2371684817036x_{59} = -94.2371684817036
x60=−2.79838604578389x_{60} = -2.79838604578389
x61=94.2371684817036x_{61} = 94.2371684817036
x62=81.6691650818489x_{62} = 81.6691650818489
x63=21.945612879981x_{63} = 21.945612879981
x64=−81.6691650818489x_{64} = -81.6691650818489
x65=−6.12125046689807x_{65} = -6.12125046689807
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to x*cos(x) + x^2*sin(x).
0cos⁡(0)+02sin⁡(0)0 \cos{\left(0 \right)} + 0^{2} \sin{\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
x2cos⁡(x)+xsin⁡(x)+cos⁡(x)=0x^{2} \cos{\left(x \right)} + x \sin{\left(x \right)} + \cos{\left(x \right)} = 0
Solve this equation
The roots of this equation
x1=−89.5465561460837x_{1} = -89.5465561460837
x2=−54.9960465516394x_{2} = -54.9960465516394
x3=−11.0848217516286x_{3} = -11.0848217516286
x4=73.8409666666368x_{4} = 73.8409666666368
x5=76.9820071395694x_{5} = 76.9820071395694
x6=45.5750212470478x_{6} = 45.5750212470478
x7=29.8785491411967x_{7} = 29.8785491411967
x8=33.0169733260496x_{8} = 33.0169733260496
x9=−76.9820071395694x_{9} = -76.9820071395694
x10=−33.0169733260496x_{10} = -33.0169733260496
x11=−7.97678462750978x_{11} = -7.97678462750978
x12=−58.1366581602094x_{12} = -58.1366581602094
x13=−4.90565966567415x_{13} = -4.90565966567415
x14=1.95588396372027x_{14} = 1.95588396372027
x15=70.6999752105956x_{15} = 70.6999752105956
x16=11.0848217516286x_{16} = 11.0848217516286
x17=−64.4181679836523x_{17} = -64.4181679836523
x18=−1.95588396372027x_{18} = -1.95588396372027
x19=−61.2773701909402x_{19} = -61.2773701909402
x20=−23.6042091422871x_{20} = -23.6042091422871
x21=−48.7152020786718x_{21} = -48.7152020786718
x22=36.1559453106627x_{22} = 36.1559453106627
x23=−36.1559453106627x_{23} = -36.1559453106627
x24=−92.6877705166201x_{24} = -92.6877705166201
x25=−73.8409666666368x_{25} = -73.8409666666368
x26=−70.6999752105956x_{26} = -70.6999752105956
x27=−14.2070931146973x_{27} = -14.2070931146973
x28=−26.7408639367464x_{28} = -26.7408639367464
x29=83.264212972531x_{29} = 83.264212972531
x30=−42.4350488166082x_{30} = -42.4350488166082
x31=−29.8785491411967x_{31} = -29.8785491411967
x32=17.3361878945599x_{32} = 17.3361878945599
x33=98.9702712571724x_{33} = 98.9702712571724
x34=14.2070931146973x_{34} = 14.2070931146973
x35=4.90565966567415x_{35} = 4.90565966567415
x36=−39.2953345326852x_{36} = -39.2953345326852
x37=7.97678462750978x_{37} = 7.97678462750978
x38=92.6877705166201x_{38} = 92.6877705166201
x39=−86.4053692621466x_{39} = -86.4053692621466
x40=−17.3361878945599x_{40} = -17.3361878945599
x41=−98.9702712571724x_{41} = -98.9702712571724
x42=61.2773701909402x_{42} = 61.2773701909402
x43=42.4350488166082x_{43} = 42.4350488166082
x44=86.4053692621466x_{44} = 86.4053692621466
x45=−95.8290096730487x_{45} = -95.8290096730487
x46=67.559039597919x_{46} = 67.559039597919
x47=64.4181679836523x_{47} = 64.4181679836523
x48=26.7408639367464x_{48} = 26.7408639367464
x49=39.2953345326852x_{49} = 39.2953345326852
x50=20.4690516301297x_{50} = 20.4690516301297
x51=58.1366581602094x_{51} = 58.1366581602094
x52=95.8290096730487x_{52} = 95.8290096730487
x53=23.6042091422871x_{53} = 23.6042091422871
x54=−80.1230908716212x_{54} = -80.1230908716212
x55=−67.559039597919x_{55} = -67.559039597919
x56=−83.264212972531x_{56} = -83.264212972531
x57=48.7152020786718x_{57} = 48.7152020786718
x58=−45.5750212470478x_{58} = -45.5750212470478
x59=−20.4690516301297x_{59} = -20.4690516301297
x60=−51.8555535655761x_{60} = -51.8555535655761
x61=80.1230908716212x_{61} = 80.1230908716212
x62=54.9960465516394x_{62} = 54.9960465516394
x63=51.8555535655761x_{63} = 51.8555535655761
x64=89.5465561460837x_{64} = 89.5465561460837
The values of the extrema at the points:
(-89.5465561460837, -8017.08607606954)

(-54.9960465516394, 3023.06608618409)

(-11.0848217516286, 121.396268979983)

(73.8409666666368, -5450.98888533752)

(76.9820071395694, 5924.72990819201)

(45.5750212470478, 2075.5839443892)

(29.8785491411967, -891.230911505695)

(33.0169733260496, 1088.62315974023)

(-76.9820071395694, -5924.72990819201)

(-33.0169733260496, -1088.62315974023)

(-7.97678462750978, -62.1728011783095)

(-58.1366581602094, -3378.37187211994)

(-4.90565966567415, 22.6751995394057)

(1.95588396372027, 2.81061592389021)

(70.6999752105956, 4996.9870697054)

(11.0848217516286, -121.396268979983)

(-64.4181679836523, -4148.20105883203)

(-1.95588396372027, -2.81061592389021)

(-61.2773701909402, 3753.41686274186)

(-23.6042091422871, 555.66382949141)

(-48.7152020786718, 2371.67212392755)

(36.1559453106627, -1305.75457696247)

(-36.1559453106627, 1305.75457696247)

(-92.6877705166201, 8589.52313790947)

(-73.8409666666368, 5450.98888533752)

(-70.6999752105956, -4996.9870697054)

(-14.2070931146973, -200.35558843529)

(-26.7408639367464, -713.577812585208)

(83.264212972531, 6931.42957649394)

(-42.4350488166082, 1799.2349627339)

(-29.8785491411967, 891.230911505695)

(17.3361878945599, -299.052908734495)

(98.9702712571724, -9793.61488616748)

(14.2070931146973, 200.35558843529)

(4.90565966567415, -22.6751995394057)

(-39.2953345326852, -1542.62517534231)

(7.97678462750978, 62.1728011783095)

(92.6877705166201, -8589.52313790947)

(-86.4053692621466, 7464.38822230175)

(-17.3361878945599, 299.052908734495)

(-98.9702712571724, 9793.61488616748)

(61.2773701909402, -3753.41686274186)

(42.4350488166082, -1799.2349627339)

(86.4053692621466, -7464.38822230175)

(-95.8290096730487, -9181.69940791564)

(67.559039597919, -4562.72446099531)

(64.4181679836523, 4148.20105883203)

(26.7408639367464, 713.577812585208)

(39.2953345326852, 1542.62517534231)

(20.4690516301297, 417.488901448924)

(58.1366581602094, 3378.37187211994)

(95.8290096730487, 9181.69940791564)

(23.6042091422871, -555.66382949141)

(-80.1230908716212, 6418.21013851154)

(-67.559039597919, 4562.72446099531)

(-83.264212972531, -6931.42957649394)

(48.7152020786718, -2371.67212392755)

(-45.5750212470478, -2075.5839443892)

(-20.4690516301297, -417.488901448924)

(-51.8555535655761, -2687.49950390865)

(80.1230908716212, -6418.21013851154)

(54.9960465516394, -3023.06608618409)

(51.8555535655761, 2687.49950390865)

(89.5465561460837, 8017.08607606954)


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=−89.5465561460837x_{1} = -89.5465561460837
x2=73.8409666666368x_{2} = 73.8409666666368
x3=29.8785491411967x_{3} = 29.8785491411967
x4=−76.9820071395694x_{4} = -76.9820071395694
x5=−33.0169733260496x_{5} = -33.0169733260496
x6=−7.97678462750978x_{6} = -7.97678462750978
x7=−58.1366581602094x_{7} = -58.1366581602094
x8=11.0848217516286x_{8} = 11.0848217516286
x9=−64.4181679836523x_{9} = -64.4181679836523
x10=−1.95588396372027x_{10} = -1.95588396372027
x11=36.1559453106627x_{11} = 36.1559453106627
x12=−70.6999752105956x_{12} = -70.6999752105956
x13=−14.2070931146973x_{13} = -14.2070931146973
x14=−26.7408639367464x_{14} = -26.7408639367464
x15=17.3361878945599x_{15} = 17.3361878945599
x16=98.9702712571724x_{16} = 98.9702712571724
x17=4.90565966567415x_{17} = 4.90565966567415
x18=−39.2953345326852x_{18} = -39.2953345326852
x19=92.6877705166201x_{19} = 92.6877705166201
x20=61.2773701909402x_{20} = 61.2773701909402
x21=42.4350488166082x_{21} = 42.4350488166082
x22=86.4053692621466x_{22} = 86.4053692621466
x23=−95.8290096730487x_{23} = -95.8290096730487
x24=67.559039597919x_{24} = 67.559039597919
x25=23.6042091422871x_{25} = 23.6042091422871
x26=−83.264212972531x_{26} = -83.264212972531
x27=48.7152020786718x_{27} = 48.7152020786718
x28=−45.5750212470478x_{28} = -45.5750212470478
x29=−20.4690516301297x_{29} = -20.4690516301297
x30=−51.8555535655761x_{30} = -51.8555535655761
x31=80.1230908716212x_{31} = 80.1230908716212
x32=54.9960465516394x_{32} = 54.9960465516394
Maxima of the function at points:
x32=−54.9960465516394x_{32} = -54.9960465516394
x32=−11.0848217516286x_{32} = -11.0848217516286
x32=76.9820071395694x_{32} = 76.9820071395694
x32=45.5750212470478x_{32} = 45.5750212470478
x32=33.0169733260496x_{32} = 33.0169733260496
x32=−4.90565966567415x_{32} = -4.90565966567415
x32=1.95588396372027x_{32} = 1.95588396372027
x32=70.6999752105956x_{32} = 70.6999752105956
x32=−61.2773701909402x_{32} = -61.2773701909402
x32=−23.6042091422871x_{32} = -23.6042091422871
x32=−48.7152020786718x_{32} = -48.7152020786718
x32=−36.1559453106627x_{32} = -36.1559453106627
x32=−92.6877705166201x_{32} = -92.6877705166201
x32=−73.8409666666368x_{32} = -73.8409666666368
x32=83.264212972531x_{32} = 83.264212972531
x32=−42.4350488166082x_{32} = -42.4350488166082
x32=−29.8785491411967x_{32} = -29.8785491411967
x32=14.2070931146973x_{32} = 14.2070931146973
x32=7.97678462750978x_{32} = 7.97678462750978
x32=−86.4053692621466x_{32} = -86.4053692621466
x32=−17.3361878945599x_{32} = -17.3361878945599
x32=−98.9702712571724x_{32} = -98.9702712571724
x32=64.4181679836523x_{32} = 64.4181679836523
x32=26.7408639367464x_{32} = 26.7408639367464
x32=39.2953345326852x_{32} = 39.2953345326852
x32=20.4690516301297x_{32} = 20.4690516301297
x32=58.1366581602094x_{32} = 58.1366581602094
x32=95.8290096730487x_{32} = 95.8290096730487
x32=−80.1230908716212x_{32} = -80.1230908716212
x32=−67.559039597919x_{32} = -67.559039597919
x32=51.8555535655761x_{32} = 51.8555535655761
x32=89.5465561460837x_{32} = 89.5465561460837
Decreasing at intervals
[98.9702712571724,∞)\left[98.9702712571724, \infty\right)
Increasing at intervals
(−∞,−95.8290096730487]\left(-\infty, -95.8290096730487\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(−xsin⁡(x)+3cos⁡(x))=0x \left(- x \sin{\left(x \right)} + 3 \cos{\left(x \right)}\right) = 0
Solve this equation
The roots of this equation
x1=−94.2795891235637x_{1} = -94.2795891235637
x2=−100.560788770886x_{2} = -100.560788770886
x3=15.8945130636842x_{3} = 15.8945130636842
x4=78.5779764426249x_{4} = 78.5779764426249
x5=25.2509941253717x_{5} = 25.2509941253717
x6=−44.0502961191214x_{6} = -44.0502961191214
x7=−87.9986725257711x_{7} = -87.9986725257711
x8=106.842221633416x_{8} = 106.842221633416
x9=87.9986725257711x_{9} = 87.9986725257711
x10=31.510845756676x_{10} = 31.510845756676
x11=−40.913898225293x_{11} = -40.913898225293
x12=−72.2981021067071x_{12} = -72.2981021067071
x13=−59.7404355133729x_{13} = -59.7404355133729
x14=−50.325024483292x_{14} = -50.325024483292
x15=62.8795272030449x_{15} = 62.8795272030449
x16=3.80876221919969x_{16} = 3.80876221919969
x17=40.913898225293x_{17} = 40.913898225293
x18=−97.4201569811411x_{18} = -97.4201569811411
x19=−25.2509941253717x_{19} = -25.2509941253717
x20=−34.6438990396267x_{20} = -34.6438990396267
x21=−47.1873806732917x_{21} = -47.1873806732917
x22=−6.70395577578075x_{22} = -6.70395577578075
x23=44.0502961191214x_{23} = 44.0502961191214
x24=−28.3796522911214x_{24} = -28.3796522911214
x25=81.7181040853573x_{25} = 81.7181040853573
x26=−53.4631297645908x_{26} = -53.4631297645908
x27=−69.1583898858035x_{27} = -69.1583898858035
x28=22.12591435735x_{28} = 22.12591435735
x29=100.560788770886x_{29} = 100.560788770886
x30=56.6016202331048x_{30} = 56.6016202331048
x31=−84.8583399660622x_{31} = -84.8583399660622
x32=−56.6016202331048x_{32} = -56.6016202331048
x33=−37.7783560989567x_{33} = -37.7783560989567
x34=−9.72402747617551x_{34} = -9.72402747617551
x35=−31.510845756676x_{35} = -31.510845756676
x36=0x_{36} = 0
x37=−15.8945130636842x_{37} = -15.8945130636842
x38=53.4631297645908x_{38} = 53.4631297645908
x39=−22.12591435735x_{39} = -22.12591435735
x40=72.2981021067071x_{40} = 72.2981021067071
x41=47.1873806732917x_{41} = 47.1873806732917
x42=84.8583399660622x_{42} = 84.8583399660622
x43=75.4379705139506x_{43} = 75.4379705139506
x44=37.7783560989567x_{44} = 37.7783560989567
x45=34.6438990396267x_{45} = 34.6438990396267
x46=50.325024483292x_{46} = 50.325024483292
x47=12.7966483902814x_{47} = 12.7966483902814
x48=−91.1390917936668x_{48} = -91.1390917936668
x49=−78.5779764426249x_{49} = -78.5779764426249
x50=6.70395577578075x_{50} = 6.70395577578075
x51=−81.7181040853573x_{51} = -81.7181040853573
x52=28.3796522911214x_{52} = 28.3796522911214
x53=−12.7966483902814x_{53} = -12.7966483902814
x54=91.1390917936668x_{54} = 91.1390917936668
x55=97.4201569811411x_{55} = 97.4201569811411
x56=−66.0188560490172x_{56} = -66.0188560490172
x57=66.0188560490172x_{57} = 66.0188560490172
x58=−62.8795272030449x_{58} = -62.8795272030449
x59=1.19245882933643x_{59} = 1.19245882933643
x60=59.7404355133729x_{60} = 59.7404355133729
x61=69.1583898858035x_{61} = 69.1583898858035
x62=9.72402747617551x_{62} = 9.72402747617551
x63=−3.80876221919969x_{63} = -3.80876221919969
x64=−19.0061082873963x_{64} = -19.0061082873963
x65=94.2795891235637x_{65} = 94.2795891235637
x66=19.0061082873963x_{66} = 19.0061082873963
x67=−75.4379705139506x_{67} = -75.4379705139506
x68=−1.19245882933643x_{68} = -1.19245882933643

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
[97.4201569811411,∞)\left[97.4201569811411, \infty\right)
Convex at the intervals
(−∞,−97.4201569811411]\left(-\infty, -97.4201569811411\right]
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
lim⁡x→−∞(x2sin⁡(x)+xcos⁡(x))=∞sign⁡(⟨−1,1⟩)\lim_{x \to -\infty}\left(x^{2} \sin{\left(x \right)} + x \cos{\left(x \right)}\right) = \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}
Let's take the limit
so,
equation of the horizontal asymptote on the left:
y=∞sign⁡(⟨−1,1⟩)y = \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}
lim⁡x→∞(x2sin⁡(x)+xcos⁡(x))=∞sign⁡(⟨−1,1⟩)\lim_{x \to \infty}\left(x^{2} \sin{\left(x \right)} + x \cos{\left(x \right)}\right) = \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}
Let's take the limit
so,
equation of the horizontal asymptote on the right:
y=∞sign⁡(⟨−1,1⟩)y = \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of x*cos(x) + x^2*sin(x), divided by x at x->+oo and x ->-oo
lim⁡x→−∞(x2sin⁡(x)+xcos⁡(x)x)=−∞sign⁡(⟨−1,1⟩)\lim_{x \to -\infty}\left(\frac{x^{2} \sin{\left(x \right)} + x \cos{\left(x \right)}}{x}\right) = - \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}
Let's take the limit
so,
inclined asymptote equation on the left:
y=−∞xsign⁡(⟨−1,1⟩)y = - \infty x \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}
lim⁡x→∞(x2sin⁡(x)+xcos⁡(x)x)=∞sign⁡(⟨−1,1⟩)\lim_{x \to \infty}\left(\frac{x^{2} \sin{\left(x \right)} + x \cos{\left(x \right)}}{x}\right) = \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}
Let's take the limit
so,
inclined asymptote equation on the right:
y=∞xsign⁡(⟨−1,1⟩)y = \infty x \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}
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:
x2sin⁡(x)+xcos⁡(x)=−x2sin⁡(x)−xcos⁡(x)x^{2} \sin{\left(x \right)} + x \cos{\left(x \right)} = - x^{2} \sin{\left(x \right)} - x \cos{\left(x \right)}
- No
x2sin⁡(x)+xcos⁡(x)=x2sin⁡(x)+xcos⁡(x)x^{2} \sin{\left(x \right)} + x \cos{\left(x \right)} = x^{2} \sin{\left(x \right)} + x \cos{\left(x \right)}
- Yes
so, the function
is
odd
The graph
Graphing y = xcosx+x^2sinx
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