# Lipschitz continuous

• Sep 4th 2011, 07:51 AM
Camille91
Lipschitz continuous
Is it true that if $f: [0;2\pi] \rightarrow \mathbb{R}$ and $f$is Lipschitz continuous then exists $C>0$ that $f'(x) \leq C$ for every $x \in [0;2\pi]$?
• Sep 4th 2011, 12:53 PM
Opalg
Re: Lipschitz continuous
Quote:

Originally Posted by Camille91
Is it true that if $f: [0;2\pi] \rightarrow \mathbb{R}$ and $f$is Lipschitz continuous then exists $C>0$ that $f'(x) \leq C$ for every $x \in [0;2\pi]$?

Being Lipschitz continuous does not imply that the derivative even exists. For example $f(x) = |x-\pi|$ is Lipschitz continuous in $[0,2\pi],$ but it is not differentiable at $\pi.$