The sum of two numbers is 48. find the maximum product and the two numbers

Kelsey S.

asked • 06/17/17

please help me answer this! for my exam! means alot

1 Expert Answer

Call one number x and the other one y.

The product of the two numbers will be x * y = xy

We can solve x + y = 32 for y.

x * y = x(32 - x) = 32x - x²

If we let the above function be f(x), then f'(x) = 32 - 2x

The maximum value of this function will occur at a critical number. A critical number occurs where f'(x) = 0 or is undefined.

f'(x) is defined for all real x.

We only need to determine where f'(x) = 0

The two numbers are 16 and 16. The maximum product is 16 * 16 = 256.

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