on the set D, a closed triangular region with vertices (0,0), (4,0), and (4,5).
Solution:
Since f is a polynomial, it is continuous on a closed bounded triangle, so there exists both an absolute maximum and minimum.
A) Find the values of f at the critical points of f in D.
No critical points exist in the interior of D. The maxima and minima occur on the boundary.
B) To find the absolute maximum and minimum we note that
is a plane so the minimum and maximum will occur at the corners of the triangle.
Since f(0,0) = 5, f(4,0) = -7 and f(4,5) = 13
the maximum is 13 and the minimum is -7.
No Maple Code for this problem.
by:sh