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Characterizing zero-derivative points (CROSBI ID 159360)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Zlobec, Sanjo Characterizing zero-derivative points // Journal of global optimization, 46 (2010), 1; 155-161. doi: 10.1007/s10898-009-9457-4

Podaci o odgovornosti

Zlobec, Sanjo

engleski

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 withouth the derivatives.

Zero-derivative point; Fermat's extreme value theorem; Theorem of Lagrange

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Podaci o izdanju

46 (1)

2010.

155-161

objavljeno

0925-5001

10.1007/s10898-009-9457-4

Povezanost rada

Ekonomija, Matematika

Poveznice
Indeksiranost