Question

Find the extreme values of f(x; y) = x2 + 3(y2) +2y
on the unit disk
x2 + y2  <=1.

Answer 1

Not sure. If x2 + y2 = 1, just the periphery, then could substitute
y = sqrt(1-x2) into f(x,y), making it g(x), then set dg/dx=0 etc.

Extreme value inside the disk would be missed this way. It's a start.