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Extrema

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
For the extrema of a differentiable function holds:

$\displaystyle f'(x_{0})$ $\displaystyle =0 \qquad \textnormal{necessary condition}$    
$\displaystyle f''(x_{0})$ $\displaystyle \ne 0 \qquad \textnormal{sufficient condition}$    
     
$\displaystyle f''(x_{0})$ $\displaystyle >0 \qquad \textnormal{minimum}$    
$\displaystyle f''(x_{0})$ $\displaystyle <0 \qquad \textnormal{maximum}$    

(Authors: Jahn/Knödler)
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  automatically generated 7/ 8/2004