Graphing y = y*cos(y)

In order to find the extrema, we need to solve the equation
$$\frac{d}{d y} f{\left(y \right)} = 0$$
(the derivative equals zero),
and the roots of this equation are the extrema of this function:
$$\frac{d}{d y} f{\left(y \right)} =$$
the first derivative
$$- y \sin{\left(y \right)} + \cos{\left(y \right)} = 0$$
Solve this equation
The roots of this equation
$$y_{1} = -12.6452872238566$$
$$y_{2} = -72.270467060309$$
$$y_{3} = 72.270467060309$$
$$y_{4} = -84.8347887180423$$
$$y_{5} = 9.52933440536196$$
$$y_{6} = 78.5525459842429$$
$$y_{7} = -6.43729817917195$$
$$y_{8} = 37.7256128277765$$
$$y_{9} = -18.90240995686$$
$$y_{10} = -56.5663442798215$$
$$y_{11} = -37.7256128277765$$
$$y_{12} = 22.0364967279386$$
$$y_{13} = -69.1295029738953$$
$$y_{14} = -28.309642854452$$
$$y_{15} = 47.145097736761$$
$$y_{16} = -97.3996388790738$$
$$y_{17} = -25.1724463266467$$
$$y_{18} = -59.7070073053355$$
$$y_{19} = -9.52933440536196$$
$$y_{20} = 6.43729817917195$$
$$y_{21} = -53.4257904773947$$
$$y_{22} = 28.309642854452$$
$$y_{23} = 91.1171613944647$$
$$y_{24} = 25.1724463266467$$
$$y_{25} = -15.7712848748159$$
$$y_{26} = -100.540910786842$$
$$y_{27} = 44.0050179208308$$
$$y_{28} = -65.9885986984904$$
$$y_{29} = 81.6936492356017$$
$$y_{30} = -116.247530303932$$
$$y_{31} = -91.1171613944647$$
$$y_{32} = -47.145097736761$$
$$y_{33} = -147.661626855354$$
$$y_{34} = -3.42561845948173$$
$$y_{35} = -50.2853663377737$$
$$y_{36} = -94.2583883450399$$
$$y_{37} = 97.3996388790738$$
$$y_{38} = -87.9759605524932$$
$$y_{39} = 94.2583883450399$$
$$y_{40} = 75.4114834888481$$
$$y_{41} = 15.7712848748159$$
$$y_{42} = 53.4257904773947$$
$$y_{43} = 69.1295029738953$$
$$y_{44} = 87.9759605524932$$
$$y_{45} = -75.4114834888481$$
$$y_{46} = -81.6936492356017$$
$$y_{47} = 3.42561845948173$$
$$y_{48} = 62.8477631944545$$
$$y_{49} = -40.8651703304881$$
$$y_{50} = 59.7070073053355$$
$$y_{51} = -78.5525459842429$$
$$y_{52} = 40.8651703304881$$
$$y_{53} = 12.6452872238566$$
$$y_{54} = -34.5864242152889$$
$$y_{55} = -31.4477146375462$$
$$y_{56} = 34.5864242152889$$
$$y_{57} = -22.0364967279386$$
$$y_{58} = 31.4477146375462$$
$$y_{59} = 50.2853663377737$$
$$y_{60} = 56.5663442798215$$
$$y_{61} = -44.0050179208308$$
$$y_{62} = 100.540910786842$$
$$y_{63} = 65.9885986984904$$
$$y_{64} = -62.8477631944545$$
$$y_{65} = 0.86033358901938$$
$$y_{66} = 18.90240995686$$
$$y_{67} = 84.8347887180423$$
$$y_{68} = -0.86033358901938$$
The values of the extrema at the points:

(-12.645287223856643, -12.6059312978927)

(-72.27046706030896, 72.2635495982494)

(72.27046706030896, -72.2635495982494)

(-84.83478871804229, 84.8288955236568)

(9.529334405361963, -9.47729425947979)

(78.55254598424293, -78.5461815917343)

(-6.437298179171947, -6.36100394483385)

(37.7256128277765, 37.71236621281)

(-18.902409956860023, -18.876013697969)

(-56.56634427982152, -56.5575071728762)

(-37.7256128277765, -37.71236621281)

(22.036496727938566, -22.0138420791585)

(-69.12950297389526, -69.1222713069218)

(-28.30964285445201, 28.2919975390943)

(47.14509773676103, -47.1344957575419)

(-97.39963887907376, 97.3945057956234)

(-25.172446326646664, -25.1526068178715)

(-59.70700730533546, 59.6986348402658)

(-9.529334405361963, 9.47729425947979)

(6.437298179171947, 6.36100394483385)

(-53.42579047739466, 53.4164341598961)

(28.30964285445201, -28.2919975390943)

(91.11716139446474, -91.1116744496469)

(25.172446326646664, 25.1526068178715)

(-15.771284874815882, 15.7396769621337)

(-100.54091078684232, -100.535938055826)

(44.005017920830845, 43.9936599791065)

(-65.98859869849039, 65.9810229367917)

(81.69364923560168, 81.6875294965246)

(-116.2475303039321, 116.243229375987)

(-91.11716139446474, 91.1116744496469)

(-47.14509773676103, 47.1344957575419)

(-147.66162685535437, 147.658240851742)

(-3.4256184594817283, 3.2883713955909)

(-50.28536633777365, -50.2754260353972)

(-94.25838834503986, -94.2530842251087)

(97.39963887907376, -97.3945057956234)

(-87.97596055249322, -87.9702777324248)

(94.25838834503986, 94.2530842251087)

(75.41148348884815, 75.4048540732019)

(15.771284874815882, -15.7396769621337)

(53.42579047739466, -53.4164341598961)

(69.12950297389526, 69.1222713069218)

(87.97596055249322, 87.9702777324248)

(-75.41148348884815, -75.4048540732019)

(-81.69364923560168, -81.6875294965246)

(3.4256184594817283, -3.2883713955909)

(62.84776319445445, 62.8398089721545)

(-40.86517033048807, 40.8529404645174)

(59.70700730533546, -59.6986348402658)

(-78.55254598424293, 78.5461815917343)

(40.86517033048807, -40.8529404645174)

(12.645287223856643, 12.6059312978927)

(-34.58642421528892, 34.5719767335884)

(-31.447714637546234, -31.4318272785346)

(34.58642421528892, -34.5719767335884)

(-22.036496727938566, 22.0138420791585)

(31.447714637546234, 31.4318272785346)

(50.28536633777365, 50.2754260353972)

(56.56634427982152, 56.5575071728762)

(-44.005017920830845, -43.9936599791065)

(100.54091078684232, 100.535938055826)

(65.98859869849039, -65.9810229367917)

(-62.84776319445445, -62.8398089721545)

(0.8603335890193797, 0.561096338191045)

(18.902409956860023, 18.876013697969)

(84.83478871804229, -84.8288955236568)

(-0.8603335890193797, -0.561096338191045)

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:
$$y_{1} = -12.6452872238566$$
$$y_{2} = 72.270467060309$$
$$y_{3} = 9.52933440536196$$
$$y_{4} = 78.5525459842429$$
$$y_{5} = -6.43729817917195$$
$$y_{6} = -18.90240995686$$
$$y_{7} = -56.5663442798215$$
$$y_{8} = -37.7256128277765$$
$$y_{9} = 22.0364967279386$$
$$y_{10} = -69.1295029738953$$
$$y_{11} = 47.145097736761$$
$$y_{12} = -25.1724463266467$$
$$y_{13} = 28.309642854452$$
$$y_{14} = 91.1171613944647$$
$$y_{15} = -100.540910786842$$
$$y_{16} = -50.2853663377737$$
$$y_{17} = -94.2583883450399$$
$$y_{18} = 97.3996388790738$$
$$y_{19} = -87.9759605524932$$
$$y_{20} = 15.7712848748159$$
$$y_{21} = 53.4257904773947$$
$$y_{22} = -75.4114834888481$$
$$y_{23} = -81.6936492356017$$
$$y_{24} = 3.42561845948173$$
$$y_{25} = 59.7070073053355$$
$$y_{26} = 40.8651703304881$$
$$y_{27} = -31.4477146375462$$
$$y_{28} = 34.5864242152889$$
$$y_{29} = -44.0050179208308$$
$$y_{30} = 65.9885986984904$$
$$y_{31} = -62.8477631944545$$
$$y_{32} = 84.8347887180423$$
$$y_{33} = -0.86033358901938$$
Maxima of the function at points:
$$y_{33} = -72.270467060309$$
$$y_{33} = -84.8347887180423$$
$$y_{33} = 37.7256128277765$$
$$y_{33} = -28.309642854452$$
$$y_{33} = -97.3996388790738$$
$$y_{33} = -59.7070073053355$$
$$y_{33} = -9.52933440536196$$
$$y_{33} = 6.43729817917195$$
$$y_{33} = -53.4257904773947$$
$$y_{33} = 25.1724463266467$$
$$y_{33} = -15.7712848748159$$
$$y_{33} = 44.0050179208308$$
$$y_{33} = -65.9885986984904$$
$$y_{33} = 81.6936492356017$$
$$y_{33} = -116.247530303932$$
$$y_{33} = -91.1171613944647$$
$$y_{33} = -47.145097736761$$
$$y_{33} = -147.661626855354$$
$$y_{33} = -3.42561845948173$$
$$y_{33} = 94.2583883450399$$
$$y_{33} = 75.4114834888481$$
$$y_{33} = 69.1295029738953$$
$$y_{33} = 87.9759605524932$$
$$y_{33} = 62.8477631944545$$
$$y_{33} = -40.8651703304881$$
$$y_{33} = -78.5525459842429$$
$$y_{33} = 12.6452872238566$$
$$y_{33} = -34.5864242152889$$
$$y_{33} = -22.0364967279386$$
$$y_{33} = 31.4477146375462$$
$$y_{33} = 50.2853663377737$$
$$y_{33} = 56.5663442798215$$
$$y_{33} = 100.540910786842$$
$$y_{33} = 0.86033358901938$$
$$y_{33} = 18.90240995686$$
Decreasing at intervals
$$\left[97.3996388790738, \infty\right)$$
Increasing at intervals
$$\left(-\infty, -100.540910786842\right]$$