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Characterizing zero-derivative points (CROSBI ID 159360)
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Zlobec, Sanjo
Characterizing zero-derivative points // Journal of global optimization, 46 (2010), 1; 155-161. doi: 10.1007/s10898-009-9457-4
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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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