Derivative Sign Patterns in Two Dimensions

Given a function defined on a subset of the plane whose partial derivatives never change sign, the signs of the partial derivatives form a two-dimensional pattern. We explore what patterns are possible for various planar domains.

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Published in:The College mathematics journal 2013-03, Vol.44 (2), p.102-108
Main Author: Schilling, Kenneth
Format: Article
Language:English
Subjects:
College Mathematics
Geometry
Mathematical analysis
Mathematical Concepts
Mathematical functions
Mathematics Instruction
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description Given a function defined on a subset of the plane whose partial derivatives never change sign, the signs of the partial derivatives form a two-dimensional pattern. We explore what patterns are possible for various planar domains.
doi_str_mv 10.4169/college.math.j.44.2.102
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source JSTOR Archival Journals and Primary Sources Collection; Taylor and Francis Science and Technology Collection; ERIC
subjects College Mathematics
Geometry
Mathematical analysis
Mathematical Concepts
Mathematical functions
Mathematics Instruction
title Derivative Sign Patterns in Two Dimensions
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