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I have a function for which I have calculated:

$\dfrac{d}{dx}f(x,y)=0 $

and

$\dfrac{d}{dy}f(x,y)=2y+\cos(y)$

How can I proceed to calculate the critical points?

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    Looks like your function only depends on $y$!2012-09-27

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Just as with equations in one variable, determine when the partial derivatives become 0. Here, one is already zero so no information there...

But the other one is $2y+\cos(y)=0$. It looks like there isn't a closed form for the solution, so you'd need an approximation...

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    You should use partial derivative notation $\frac{\partial}{\partial x} f(x,y) = 0$, etc.2012-09-27