xtreme values of multivariable functions

I'm supposed to find the absolute extreme values taken on by f on the set of D.

f (x, y) = 2x^2+y^2−4x−2y+2, D = {(x, y) : 0 ≤ x ≤ 2,0 ≤ y ≤ 2x}.

Could someone please teach me how to do this. The book doesn't really do it for me. I need to figure out how to find the extreme values.

partial derivatives, solve for df/dx = 0, df/dy = 0, then check endpoints too.