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Math Help - proving that f' is bounded

  1. #1
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    proving that f' is bounded

    The problem I am trying to solve is
    f:\Re\rightarrow\Re is a differentiable function and it has a continuous derivative. I need to prove that f' is bounded on [a,b] where -\infty<a<b<\infty.

    I have shown that if f:X\rightarrow Y is continous on X and if A is a compact subset of X that f(A) is also compact. But have no clue if this will help of where to go from here.

    Thanks in advance
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  2. #2
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    Re: proving that f' is bounded

    Quote Originally Posted by klw289 View Post
    The problem I am trying to solve is
    f:\Re\rightarrow\Re is a differentiable function and it has a continuous derivative. I need to prove that f' is bounded on [a,b] where -\infty<a<b<\infty.

    I have shown that if f:X\rightarrow Y is continous on X and if A is a compact subset of X that f(A) is also compact. But have no clue if this will help of where to go from here.
    It tells you "it has a continuous derivative..
    Any continuous function is bounded on a compact set.
    Any interval [a,b] is compact.
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