Math notation for location of the maximum
Given a function $f(x)$, we can normally find $\max_i f(i)$. This expression evaluates to the maximum value of $f(x)$. Sometimes, however, what is interesting isn't as much the maximum value itself, but the value at which the function reaches its maximum, whatever that might be:
In plain English, I want to know who has eaten the most $f$ruit, rather than how much he's eaten.
This is kind of cumbersome, and perhaps needlessly requires a new symbol t. Besides, this isn't entirely correct, as $f(x)$ could very well have more than one maximum:
Is there a nicer way to express this concept?