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Thread: differentiability of function g

  1. #1
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    differentiability of function g

    Suppose g is a function continuous on the closed and bounded interval
    [a, b], b > a > 0 and differentiable on the open interval (a, b).
    Prove that there exists a point β in (a, b) such that
    \frac{bg(a)-ag(b)}{b-a} = g(\beta) - \beta{g'(\beta).

    I tried to use the Mean Value Theorem, but I could not arrive at the answer.
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  2. #2
    Junior Member MathVideos's Avatar
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    Re: differentiability of function g

    Think about the mean value of g(x) and the mean value of g'(x). Remember, g'(x) has to, at one point, be equal to the average rate of change g(x)
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