# A Surface with One Local Minimum

A smooth surface in $\Re^2$ or $\Re^3$ has one critical point that is a local, but not global minimum. Must that surface have another critical point? While the answer in the 2-D version is "yes", in 3-D the answer is "no", as illustrated by examples in this paper. The authors further analyze for which surfaces the answer is "yes" in 3-D.

Old Node ID:
1898
Author(s):
J. Marshall Ash (DePaul University) and Harlan Sexton
Publication Date:
Tuesday, June 10, 2008
Original Publication Source:
Mathematics Magazine
Original Publication Date:
May, 2008
Subject(s):
Calculus
Several Variable Calculus
Number Concepts
Topic(s):
Optimization
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Publish Page:
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File Content:
Rating Count:
9.00
Rating Sum:
33.00
Rating Average:
3.67
Author (old format):
J. Marshall Ash and Harlan Sexton
Applicable Course(s):
3.3 Mainstream Calculus III, IV