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Math Help - Derivative help

  1. #1
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    Derivative help

    So I'm completely lost on this question and I'm not sure where to start any help would be greatly appreciated. Here is the question: find a function f(x) that is continuous at x=1,2 and 3 but not differentiable at x=1,2 and 3. Comment: it has to be one such function not three functions. Thanks for the help.
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  2. #2
    Senior Member x3bnm's Avatar
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    Re: Derivative help

    Quote Originally Posted by ethandf06 View Post
    So I'm completely lost on this question and I'm not sure where to start any help would be greatly appreciated. Here is the question: find a function f(x) that is continuous at x=1,2 and 3 but not differentiable at x=1,2 and 3. Comment: it has to be one such function not three functions. Thanks for the help.
    For that you can have piecewise functions(like ceil or floor) which are:

    f(x) = \lceil{x}\rceil \text{ or } g(x) = \lfloor{x}\rfloor

    continuous at x = 1, 2, 3 but not differentiable at these locations.

    The plot is given below:

    Derivative help-piecewise_func.jpg
    Last edited by x3bnm; April 12th 2013 at 03:15 AM.
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  3. #3
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    Re: Derivative help

    Quote Originally Posted by ethandf06 View Post
    So I'm completely lost on this question and I'm not sure where to start any help would be greatly appreciated. Here is the question: find a function f(x) that is continuous at x=1,2 and 3 but not differentiable at x=1,2 and 3. Comment: it has to be one such function not three functions. Thanks for the help.
    Here is such a function that is continuous everywhere.
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