Question

5. Find two numbers whose sum is 32 and product is 255​

Answer 1

Answer:

Call one number x and the other one y.

x + y = 32

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

We can solve x + y = 32 for y.

y = 32 - x

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

32 - 2x = 0

32 = 2x

x = 16

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

Hope it helps :)