Find absolute maximum and minimum of the function
$f(x,y)=3-x^2+y^2$
on the region
$R = \{(x,y):1≥x≥0, 2≥y≥0\}$
I found that the gradient is
$∇f(x,y)=(2x,2y)$
and that the critical point inside the domain is (0,0) and it is a local minimum. I know I have to check the boundary, and I know how to do it for a fixed equation like $x^2+y^2=1$ but not for the domain I'm given. Can someone explain how this type of problem is to be solved? I don't seem to understand this problem logically or intuitively.