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Math Help - Mean Value Theorem

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    Mean Value Theorem

    is this statement true?
    If f'(x)=0 for all in an interval (a, b), then f(x)=0 for all x in the interval (a, b).
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  2. #2
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    Quote Originally Posted by Baatata View Post
    is this statement true?
    If f'(x)=0 for all in an interval (a, b), then f(x)=0 for all x in the interval (a, b).
    what would be the value of f'(x) in (a,b) if f(x) = 1 ?
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  3. #3
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    Quote Originally Posted by Baatata View Post
    is this statement true?
    If f'(x)=0 for all in an interval (a, b), then f(x)=0 for all x in the interval (a, b).
    No, f could be another constant.
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  4. #4
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    If f(x)=0 implies that f'(x)=0 .
    However, the same can be said for any constant c.
    Thus, f(x) = c implies that f'(x)=0.
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