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Math Help - question about continuous function.

  1. #1
    Newbie taypen's Avatar
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    question about continuous function.

    hello,

    i got continuous function on [0,1] such that f(0) = f(1) i need to prove that exist "a" such that f(a) = f(a+0.5)
    a\in \left[0,\frac{1}{2}\right]

    your help would be much appreciated!
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  2. #2
    MHF Contributor
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    Re: question about continuous function.

    The idea is described in the Wikipedia article about the intermediate value theorem.
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  3. #3
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    Re: question about continuous function.

    Emakarov is correct. Look at the example at the bottom of the article concerning real world applications. Your problem is just a slight variation: consider the function g(t)=f(t)-f(t+0.5).
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  4. #4
    Newbie taypen's Avatar
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    Thumbs up Thanks

    I knew it was something around the intermediate value theory
    After reading all the article i found simmilar problem and it's solution.
    So thanks for your help.
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