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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)

Examples:

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  automatically generated 4/ 8/2008