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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: 
Furnished by JSTOR: 
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
4.0 Advanced Mathematics
Modify Date: 
Thursday, August 9, 2012
Average: 3.7 (9 votes)

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