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

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

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A function

has a global minimum at $a \in D$ , iff

$\displaystyle f(a) \le f(x)\quad \forall x\in D .$

For a local minimum is suffices that the value

be the smallest value in some local neighborhood $(a-\delta,a+\delta)\cap D$ .

Global and local maximum is defined analogously.

$\includegraphics[width=0.6\linewidth]{Beispiel_Extrema.eps}$

For piecewise continuously differentiable functions on closed intervals, extrema can only appear at those points $b \in D$ for which , at those points $b \in D$ for which is discontinuous, or at boundary points. Their type can be determined by examining higher derivatives as well as by comparing various values of the function.

(Authors: Höllig/Hörner/Abele)

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automatically generated 1/9/2017