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Math Help - Rolle's theorem

  1. #1
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    Rolle's theorem

    Rolle's theorem requires three conditions be satisfied:
    i. f is continuous on [a,b]
    ii. f is differentiable on (a,b), and
    iii. f(a)=f(b)

    Find three functions that satisfy exactly two of these three conditions, but for which the conclusion of Rolle's theorem does not follow. That is, there is no point c element of (a,b) such that f](c) = o
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  2. #2
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    Quote Originally Posted by luckyc1423 View Post
    Rolle's theorem requires three conditions be satisfied:
    i. f is continuous on [a,b]
    ii. f is differentiable on (a,b), and
    iii. f(a)=f(b)

    Find three functions that satisfy exactly two of these three conditions, but for which the conclusion of Rolle's theorem does not follow. That is, there is no point c element of (a,b) such that f](c) = o
    f(x)=|x| on [-1,1]
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by ThePerfectHacker View Post
    f(x)=|x| on [-1,1]
    violates condition ii, but satisfies the other two.

    f(x) = x on [0,1]

    satisfies conditions i and ii, but not condition iii.
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