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Math Help - Mean Value Theorem (Confused)

  1. #1
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    Mean Value Theorem (Confused)

    The geometric mean of two positive numbers
    a and b is the number sqrt(ab).
    Show that the value c in the conclusion of the Mean Value Theorem for f(x)= 1/x on the interval of positive numbers [a,b]is c = sqrt(ab).

    I understand other problems with M.V.T. but I don't know how to aproach this one.

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  2. #2
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    Sep 2009
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    Try writing it out:
    What is f'(x)?
    f'(x)=\left(\frac{1}{x}\right)'=-\frac{1}{x^2}

    So the mean value theorem says:

    f(b)-f(a)=f'(c)(b-a)

    It is just simple algebra now.
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