Find two numbers whose sum is 16 and whose product is a maximum.
Two numbers whose sum is 16 and whose product is a maximum have to be determined. Let one of the numbers be X, the other number is (16 - X)
The product of the numbers is P = X*(16 - X) = 16X - X^2
To maximize the product solve P' = 0
=> 16 - 2X = 0
=> X = 8
The two numbers are 8 and 8
check Approved by eNotes Editorial