# Math Help - Lipschitz continuous

1. ## 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 $x \in [0;2\pi]$?

2. ## Re: Lipschitz continuous

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 $\pi.$