The ebook Elementary Calculus is based on material originally written by H.J. Keisler. For more information please read the copyright pages.


Extreme Value Theorem

EXTREME VALUE THEOREM

Suppose z - f(x, y) is continuous at every point of a closed region D. Then the function f with its domain restricted to D has a maximum and a minimum.

The proof is similar to the corresponding proof for one variable.


Last Update: 2006-11-05