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

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- Sep 4th 2011, 06:51 AMCamille91Lipschitz continuous
Is it true that if $\displaystyle f: [0;2\pi] \rightarrow \mathbb{R}$ and $\displaystyle f$is Lipschitz continuous then exists $\displaystyle C>0$ that$\displaystyle f'(x) \leq C $ for every $\displaystyle x \in [0;2\pi] $?

- Sep 4th 2011, 11:53 AMOpalgRe: Lipschitz continuous