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Math Help - Proof of a maximum and minimum

  1. #1
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    Proof of a maximum and minimum

    A function f is said to be increasing on a set S if the inequality f(t) is less than or equal to f(x) holds whenever t and x belong to S and t is less than or equal to x. Prove that every increasing function on the interval [0,1] must have both a max and a min.
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  2. #2
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    What can you say about f(1)? And what can you say about f(0)?
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  3. #3
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    Quote Originally Posted by Slazenger3 View Post
    A function f is said to be increasing on a set S if the inequality f(t) is less than or equal to f(x) holds whenever t and x belong to S and t is less than or equal to x. Prove that every increasing function on the interval [0,1] must have both a max and a min.
    Do you want to say that the max/min occurs on the interval?
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  4. #4
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    I believe so...
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  5. #5
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    Then look again at JoachimAgrell's response!
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  6. #6
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    Quote Originally Posted by Slazenger3 View Post
    I believe so...
    To give a further hint:

    Take any number in [0,1], say c. Now compare f(c) to f(0) and f(1).
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