#### Question

Find two numbers whose sum is 24 and whose product is as large as possible.

#### Solution

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

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Solution Find Two Numbers Whose Sum is 24 and Whose Product is as Large as Possible. Concept: Maxima and Minima.