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I have a function as below,
$f(\alpha) = \frac{{1 - \alpha }}{2}\ln \left( {1 + \frac{{AB}}{{B + \frac{{1 - \alpha }}{{C\alpha }}}}} \right)$,
where $A$, $B$, $C$ are constant, and $0 < \alpha < 1$ is a variable. Can someone give me a hint how to derive a value of $\alpha$ that maximizes the given function.
I have tried to solve this way:
$\frac{{df\left( \alpha \right)}}{{d\alpha }} = 0$,
but I could not get a closed form solution.

Thank you very much. Best regards, Binh.

BinhDDT
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  • There is no closed form solution for the solution of $\frac{{df\left( \alpha \right)}}{{d\alpha }} = 0$. If you have the values of $A,B,C$ use Newton for the solution. If you give me numbers, I shall show you how to proceed. – Claude Leibovici Jan 27 '14 at 08:31

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