# differentiability of function g

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• April 2nd 2012, 02:42 AM
alphabeta89
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.
• April 2nd 2012, 04:21 AM
MathVideos
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)