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Nonconstant Continuous Functions whose Tangential Derivative Vanishes along a Smooth Curve

Published online by Cambridge University Press:  20 November 2018

Laurent Moonens
Laurent Moonens*
Affiliation:
Département de mathématique, Université catholique de Louvain, 1348 Louvain-la-neuve, Belgium e-mail: laurent.moonens@uclouvain.be
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Abstract

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We provide a simple example showing that the tangential derivative of a continuous function $\phi $ can vanish everywhere along a curve while the variation of $\phi $ along this curve is nonzero. We give additional regularity conditions on the curve and/or the function that prevent this from happening.

Keywords

26A2428A15

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 54 , Issue 4 , 01 December 2011, pp. 706 - 715
Copyright
Copyright © Canadian Mathematical Society 2011

References

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