PROBLEM: Find maximum and minimum values of the
function
f x , y=x y−5 y−25 x125
on the region on or above y=x2 and on or below y = 28.
The boundaries of the surface on the given domain are given
by the following space curves:
〈 x , x 2 , x 3−5 x 2−25 x125〉 for − 28≤x≤  28 (black curve)
〈 x , 28,3x−15〉 for − 28≤x≤  28
(blue curve)
From the graph we can see that a minimum is obtained at
one endpoint of the blue curve.
The absolute maximum is on the black curve and it can be
determined by finding the maximum of z=x 3−5x 2−25 x125 .


Absolute Maximum:
5 25
f − ,
=148.148
3 9
Absolute Minimum:
f − 28 , 28=−30.874