Mo logo [home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff] german flag
Mathematics-Online lexicon:

Condition for Extremum

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z overview
A $ n$ -times continuously differentiable function $ f$ with

$\displaystyle f'(a) =f''(a)=\cdots=f^{(n-1)}(a)=0$   and$\displaystyle \quad f^{(n)}(a) \neq 0\,, $

has an extremum at $ a$ iff $ n$ is even. In this case $ f$ has a local maximum (minimum) at $ a$ , if $ f^{(n)}(a)<0$ ( $ f^{(n)}(a)>0$ ).
(Authors: App/Höllig/Abele)

Annotation:

[Examples] [Links]
  automatically generated 4/ 8/2008