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"The Only Critical Point in Town" Test

by Ira Rosenholtz (University of Wyoming) and Lowell Smylie (University of Wyoming)

This article originally appeared in:
Mathematics Magazine
May, 1985

Subject classification(s): Calculus | Several Variable Calculus
Applicable Course(s): 3.3 Mainstream Calculus III, IV | 4.11 Advanced Calc I, II, & Real Analysis

If a function of one variable has a unique critical point, then it is not only a local max/min, but global. Does the same hold for functions of two variables? The authors provide a counterexample.

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Capsule Course Topic(s):
Multivariable Calculus | Optimization
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