(819,#3) Find the local maximum and minimum values and the saddle point of the function .

Solution:

To find the critical points, solve the equations:

Substituting B into A,

Therefore, there is one critical point (0,-1)

Using the Second Derivative Test,

So, f (0,-1) = -1 is a local minimum.

Here is a graph of the negative of the function where the minimum of f(x,y) is displayed as a maximum of -f (x,y).

Maple code

by:sh