What is the largest possible product you can form from two non-negative numbers whose sum is 66? The maximum product is

Question

What is the largest possible product you can form from two non-negative numbers whose sum is 66? 

The maximum product is

Answer 1

If the 2 numbers had a sum of 50, then one would be x and the other would be 50 - x.

Their product would be f(x) = x50 - x) = -x^2 + 50x.

This is a parabola which opens downward, with f’(x) = -2x + 50, so the maximum occurs when x = 25.