Find the absolute maximum of the function f(x,y) = x^2 + 4y on the set of points (x,y) that satisfy x^2 + y^2 < or = to 25. I understand that you have to check the endpoints and find critical points, but I cannot solve this. Thank you.

Answer 1

take a look here

http://math.stackexchange.com/questions/1572835/finding-the-max-and-min-values-for-a-surface-on-region-r

and I think you will be able to get going. Google can also provide many other examples.