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Mathematics-Online course: Preparatory Course Mathematics - Analysis - Extrema and Curve Sketching

Test for Extrema

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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)

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  automatically generated 1/9/2017