I have a function that I am trying to find for what input it maximizes.
$$ f(n) = {\binom{S}{2}}^{n/S}$$
I need to find the $S$ for which this function maximizes (for infinite $n$). more generally, I need to find the correct $S$ for each given $m$. (in this case $m=2$)
$$ f(n) = {\binom{S}{m}}^{n/S}$$
I think that for the first equation the result is $S=5$ but I am not sure..
How do I approach the second problem? how can I find the maximum based on 2 variables?
EDIT n,S and m are integers.