Thread: local minimum and maximum values

Find the local minimum and local maximum values of the function
f(x,y) = 4xy - x^4 - y^4

I only got 3 critical points is that correct?

3 looks right to me. Then, I seem to remember my Calc book having some crazy second-derivative test for ensuring they're extremes.

Originally Posted by Mazerakham

3 looks right to me. Then, I seem to remember my Calc book having some crazy second-derivative test for ensuring they're extremes.

Using the second derivatives test I got one saddlepoint at (0, 0) and maximum at (1, 1) and (-1, -1)