 # f(x,y)=x\sin(x)+\cos(x)-y\sin(x)+\frac{y^2}{2} My task is to find the critical points of t poveli1e 2022-01-25 Answered
$f\left(x,y\right)=x\mathrm{sin}\left(x\right)+\mathrm{cos}\left(x\right)-y\mathrm{sin}\left(x\right)+\frac{{y}^{2}}{2}$
My task is to find the critical points of this multivariable function (Determine the set of critical points of the function). Now I found the partial derivative to be${f}_{x}^{\prime }=\left(x-y\right)\mathrm{cos}\left(x\right)$
${f}_{y}^{\prime }=y-\mathrm{sin}\left(x\right)$
Wolfram Alpha says the critical point(s) is/are at $x=y$? How do I get the above in that form? The best I could do was get it in the form $x-y\mathrm{sec}\left(x\right)+\mathrm{tan}\left(x\right)=y$
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Only one critical point is located on the line $y=x$. There are an infinite number of critical points on the lines $y=±1$
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