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.

Rough sketch, mate.

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

Alright well >>3 is the answer but it doesn't tell you much.

Think back to calc 1 where to find the relative extrema of a function you just differentiate it and solve the derivative for f'(x)=0? (If you don't, the reasoning is that the slope of a curve at a peak is a horizontal tangent, which has slope 0, so solve f'(x) = 0 for x).

Well, for multivariable functions, the principle is the same but just extended.