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Math Help - differentiable function

  1. #1
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    differentiable function

    Question: True or False, Justify.
    There does not exist a differentiable function f: \Re-> \Re such that f(-1)=9, f(3)=1 and f'(x) \geq-1 for all x \in [-1,3].

    I think this is false because in order to have a derivative of -1, you would have to have an original function as a line with a slope of -1, but there is only one line between these two points and that slope is -2.

    What do you think?
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: differentiable function

    Quote Originally Posted by CountingPenguins View Post
    Question: True or False, Justify.
    There does not exist a differentiable function f: \Re-> \Re such that f(-1)=9, f(3)=1 and f'(x) \geq-1 for all x \in [-1,3].

    I think this is false because in order to have a derivative of -1, you would have to have an original function as a line with a slope of -1, but there is only one line between these two points and that slope is -2.

    What do you think?

    Use LaGrange theorem.
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  3. #3
    Super Member TheChaz's Avatar
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    Re: differentiable function

    Quote Originally Posted by Also sprach Zarathustra View Post
    Use LaGrange theorem.
    Most would call this the "Mean Value Theorem" (which is what should be used )

    @Penguins, you are correct. No such function exists with the stated properties. Hope you can prove it!
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