how do I initialize a float to its max/min value?

You can use std::numeric_limits which is defined in <limits> to find the minimum or maximum value of types (As long as a specialization exists for the type). You can also use it to retrieve infinity (and put a - in front for negative infinity).

#include <limits>

//...

std::numeric_limits<float>::max();
std::numeric_limits<float>::min();
std::numeric_limits<float>::infinity();

As noted in the comments, min() returns the lowest possible positive value. In other words the positive value closest to 0 that can be represented. The lowest possible value is the negative of the maximum possible value.

There is of course the std::max_element and min_element functions (defined in <algorithm>) which may be a better choice for finding the largest or smallest value in an array.