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Mathematik-Online problems:

Problem 476: Differentiability of a Linear Function

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 function $ f$ be differentiable at $ x_0\in\mathbb{R}$ and let $ f$ further suffice the equation $ f(x+y)=f(x)+f(y)$ for all $ x,y\in\mathbb{R}$ .
a)
Use the difference quotient to show that $ f$ is differentiable for all $ x \in \mathbb{R}$.
b)
Prove the existence of a constant $ a\in \mathbb{R}$ with $ f(x)=ax$ for all $ x \in \mathbb{R}$.
(Authors: Wipper/Abele)
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  automatisch erstellt am 21.  4. 2006