Find two numbers whose sum is 24 and whose product is as large as possible.
Let one number be x. Then, the other number is (24 − x).
Let P(x) denote the product of the two numbers. Thus, we have:
∴By second derivative test, x = 12 is the point of local maxima of P. Hence, the product of the numbers is the maximum when the numbers are 12 and 24 − 12 = 12