(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm supposed to find (and classify, which I'm really not sure what that means) critical points of f(x,y) = x^{2}y- x^{2}- 2y^{2}- 2x^{4}- 3y^{4}

2. Relevant equations

3. The attempt at a solution

I found the partial derivatives,

f_{x}(x,y) = 2xy - 2x - 8x^{3}

and

f_{y}(x,y) = x^{2}- 4y - 12y^{3}

I gather that x = 0 and x = sqrt(y-1/4)

I can't figure out how to solve for y, if I'm even supposed to.

I was under the impression to set both equations to 0 and solve, but I don't know if I am correct.

I guess my [STRIKE]main[/STRIKE] only question is if I am supposed to take the y solution and use it in the x? I want to solve it 100% on my own, so I only want broad answers, if that makes any sense?

Thanks to anyone who can help me! :)

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# Finding Critical Points of a multivariable function

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