on the set D,
a region bounded by the parabola
and the line
Solution:
A) Find the values of
at the critical points of
D.
The value at the critical point (1,1) is 0. As we shall see this neither an absolute maximum or minimum on D.
B) Find the values of
at the critical points of
D.
On L2, 
.
Define g by
Plotting g(x) we see that it has a maximum at 2 and a minimum at -2.
To continue define h by
.
This function is a line.
For x = -2 it has a minimum of -9; for x = 2 it has a maximum of 3.
Combining this with the results of g(x), and the fact that f(1,1) = 0, we see that the function f(x,y) has a global minimum of -9 at x = - 2, y = 4 and a global maximum of 3 at x = 2, y = 4.
No Maple Code for this problem.
by:sh