Solution:

A) Find the values of at the critical points of D.

Therefore, is the only critical point in the disk.

Since,

It follows that (0,0) is a saddle point.

B) On the boundary of D we have so

The graph of g(x) shows that the function has its minimum at x = -1 and maximum at x = 1.

Since x = -1 corresponds to y = 0, the function f(x,y) will have a minimum value of -2 at (x, y) = (-1,0) . Similarly f(x,y) has a maximum of 2 at (x,y) = (1,0).

No Maple Code for this problem.