Let . Find the absolute maximum and absolute minimum of f on the region

So I tried to find critical points, and the only ones are , which are not in the region , so now I have to find the extrema on the boundary. This is where I am having much trouble. I tried doing both and , and I end with pretty nasty equations that seem impossible (or at least extremely difficult) if I set their derivatives equal to 0. Any tips/work shown would be greatly appreciated.