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JGO
2010

Characterizing zero-derivative points

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Characterizing zero-derivative points
We study smooth functions in several variables with a Lipschitz derivative. It is shown that these functions have the “envelope property”: Around zero-derivative points, and only around such points, the functions are envelopes of a quadratic parabolloid. The property is used to reformulate Fermat’s extreme value theorem and the theorem of Lagrange under slightly more restrictive assumptions but without the derivatives. Keywords Zero-derivative point · Fermat’s extreme value theorem · Theorem of Lagrange Mathematics Subject Classification (2000) 26B05 · 90C30
Sanjo Zlobec
Added 28 Jan 2011
Updated 28 Jan 2011
Type Journal
Year 2010
Where JGO
Authors Sanjo Zlobec
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