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Math Help - Its an entrance exam problem based on Calculus

  1. #1
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    Its an entrance exam problem based on Calculus

    Let f : R -> R be a continuous function such that f(x + 1) = f(x), for all x. Then f
    attains its supremum. Is this statement true or false?? Give reasons...???
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  2. #2
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    Re: Its an entrance exam problem based on Calculus

    Well, f attains its supremum on [0,1]...
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  3. #3
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    Re: Its an entrance exam problem based on Calculus

    could you please elaborate
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  4. #4
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    Re: Its an entrance exam problem based on Calculus

    See the extreme value theorem. And the values of f on \mathbb{R}\setminus[0,1] are the same as on [0, 1].
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