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    Lipschitz continuous

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

    Quote Originally Posted by Camille91 View Post
    Is it true that if f: [0;2\pi] \rightarrow \mathbb{R} and fis 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.
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