Next: About this document ... Up: No Title Previous: No Title
The purpose of this lab is to acquaint you with techniques for
finding and classifying local and global extreme values of
functions of two variables. A crucial first step in solving such
problems is being able to find and classify local extreme points
of a function. What we mean by the term local extreme values is
contained in the following definition. Let f be a function
defined at a point (x0,y0). Then f(x0,y0) is a local maximum if
for all (x,y) in an open disk containing ( x0,y0) and f(x0,y0)
is a local minimum if for all (x,y) in an open disk containing (
x0,y0). If f(x0,y0) is a local maximum or a local minimum, we
say that it is a local extreme value. In single-variable
calculus, we found that the first derivative vanished at a local
extreme value. For functions of two variables, both first-order
partial derivatives vanish as described by the following
theorem. If a function f has a local extreme value at a point
(x0,y0) and the partial deri