Question

Find the maximum and minimum product of 2 numbers who sum is 5

Answer 1

y = x(5-x) = 5x - x^2
y' = 5-2x
y'=0 when x = 5/2

Answer 2

max product: (5/2)^2 = 25/4
min product: 0*5 = 0

assuming x >= 0

allowing negative values means there is no minimum product. For example, -100 * 105 = -10500.