## how to prove a function has a minimum

Hello all,

I have a complex function
$F(x)=\frac{(a^x-1)^m}{2a/m}\sum_{ D(s)}(\frac{1}{1-x})^m \prod_{r\in d(s)} \frac{m(2^{2x^2}-1)}{2^n-1}$

How can I prove that it has a minimum at certain point.
Derivating the above function seems to be complex.
Can anyone give me some suggestions for finding the minimum.

Thanks