I have the following problem to find critical points for and note whether I have any local minimas, saddle points, or local maximas.

$\displaystyle f(x,y)=x^2y+2y^2-2xy+6$

I found the following partial derivatives:

$\displaystyle f_{x}=2xy-2y$ and $\displaystyle f_{y}=x^2+4y-2x$

Solving $\displaystyle 2xy-2y=0$, I got: $\displaystyle y=0$ and $\displaystyle x=1$

BUT, I can't figure out all of the points for:

$\displaystyle x^2+4y-2x=0$

I'm getting: $\displaystyle y=\frac{1}{2}x-\frac{x^2}{4}$ ??

How do you get any critical points from that?

Any assistance will be appreciated!

Thank you in advance!

Jen