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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 $ [0,1]$ and differentiable for $ (0,1)$. 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 $ g'$ has a root within $ (0,1)$?

(Authors: Kimmerle/Höfert)

Solutions:


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  automatisch erstellt am 14. 10. 2004