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Math Help - Continuous function

  1. #1
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    Continuous function

    f: [0,2]--->R be a continuous function on [0,2]. And f(0)=f(2).
    Show that there is a c in (0,1) such that f(c)=f(c+1).

    (hint: g(x)=f(x)-f(x+1))
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  2. #2
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    Quote Originally Posted by alper82 View Post
    f: [0,2]--->R be a continuous function on [0,2]. And f(0)=f(2).
    Show that there is a c in (0,1) such that f(c)=f(c+1).

    (hint: g(x)=f(x)-f(x+1))
    Note that:

    1. g(0) = f(0) - f(1) and g(1) = f(1) - f(2) = f(1) - f(0) = - g(0).

    2. g(x) is continuous.

    Apply the Intermediate Value Theorem.
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