Mathematik-Online problems: Problem 117: Generalized Mean Value Theorem

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	Mathematik-Online problems:
	Problem 117: Generalized Mean Value Theorem

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

Let the functions $f: [0,1]\longrightarrow\mathbb{R}$ and $g:[0,1]\longrightarrow\mathbb{R}$ be continuous for

and differentiable for

. Also let $g'(x)\neq 0$ for all $x\in (0,1)$ .

Proof: There is a $\xi\in (0,1)$ so that

$\displaystyle \frac{f'(\xi)}{g'(\xi)} = \frac{f(1)-f(0)}{g(1)-g(0)}\,.$

Is this true, if

has a root within

(Authors: Kimmerle/Höfert)

Solutions:

automatisch erstellt am 14. 10. 2004