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.