Let x and y represent the two numbers that add up to 24.
x + y = 24
=> y = 24 - x
The product of the two numbers is P = x*y = x*(24 - x) = 24x - x^2.
To maximize the product P, solve P' = 0 for x.
P' = 24 - 2x
24 - 2x = 0
=> x = 12
Also P'' = -2 which is negative
for x = 12
The product when x = 12 is 12*12 = 144
hope it helps!
