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Math Help - Mean Value Theorem

  1. #1
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    Mean Value Theorem

    Verify that the function satisfies the hypotheses (or conditions) of the Mean Value Theorem on the given interval. Then find all numbers c that satisfy the conclusions of the Mean Value Theorem.
     f(x) = 1/x,   [1, 3]

    Thank you in advance if anyone can help
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  2. #2
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    Quote Originally Posted by ilovemymath View Post
    Verify that the function satisfies the hypotheses (or conditions) of the Mean Value Theorem on the given interval. Then find all numbers c that satisfy the conclusions of the Mean Value Theorem.
     f(x) = 1/x,   [1, 3]

    Thank you in advance if anyone can help
    what is the hypothesis of the MVT? once you determine if the function satisfies the hypothesis over the given interval ...

    f'(c) = \dfrac{f(b) - f(a)}{b-a}
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  3. #3
    Senior Member Sambit's Avatar
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    The hypotheses of Mean Value Theorem ensures that
    (i) The function 'f' is continuous in the closed interval[1,3] and
    (ii)The function 'f' is differentiable in the open interval(1,3).

    Now what can you say about the differentiability and continuity of the function f(x)=\frac{1}{x} for the given intervals?
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