Naslov
On the Behaviour of Functions around Zero-Derivative Points

Autori
Zlobec, Sanjo

Izvornik
International journal of optimization: theory, methods and applications (2070-5565) 1 (2009), 4; 329-340

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
zero-derivative point; Fermat's extreme value theorem; mean value theorem; Lagrange multiplier theorem

Sažetak
Zero-derivative points are of the fundamental importance in calculus and otimization. It has been recently shown that on intervals around zero-derivative points, and only around zero-derivative points, every smooth function with a Lipschitz derivative is an "envelope" of a parabolloid. In this paper we give two equivalent, but geometrically different, reformulations of this result. They are applied to the three classic theorems: Fermat's extreme value theorem, the mean value theorem, and the Lagrange multiplier theorem. These theorems are augmented over intervals and stated withouth derivatives.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Ekonomija

POVEZANOST RADA