- #1

arisachu

- 3

- 0

## Homework Statement

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}

## Homework Equations

## 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! :)

Last edited: