Finding a maximum of a discrete function

I would like to find a (local) maximum of the function f(n), where f(n) is real, and n is a natural number (n=1,2,...). The function f(n) is a quite complex composite of linear, quotient and exponential functions, but has only a single maximum. The classical method based on the a derivative (quotient, chain, power rules) does not work since n is not a real number.
How to find a maximum in a simple way?
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