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Math Help - example of a function that is continuous but not differentiable

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    example of a function that is continuous but not differentiable

    I need an example of a function that is continuous at some x0 but not differentiable at x0.

    is f(x) = |x| a right answer?
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by dgmath View Post
    I need an example of a function that is continuous at some x0 but not differentiable at x0.

    is f(x) = |x| a right answer?
    Yes. Or a uniformly continuous function which is nowhere differentiable. In fact, given a continuous function f:I\to\mathbb{R} you may construct a continuous function g:I\to\mathbb{R} such that \|f-g\|_{\infty}<\varepsilon for some fixed but arbitrary \varepsilon>0 and which is nowhere differentiable. Your answer also shows that given a function f which is differentiable at x_0 that the function f(x)+|x-x_0| is not differentiable at x=x_0 giving and infinitely weaker form of the aforementioned theorem.
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