(819,#5) Find the local maximum and minimum values and saddle points of the function

Solution:

To find the critical points, solve the equations:

Substituting the values x = 0, y = -1 into B:

Therefore, the critical points are

Using the Second Derivative Test,

So, f(0,0) = 4 is a local minimum and are saddle points.

Here is a graph of the function -f(x,y) where the local minimum of f(x,y) is displayed as a maximum of -f(x,y). The saddle points at are also evident.

Maple code

by:sh