Question

Find two positive numbers whose product is 64 and whose sum is a minimum. (If both values are the same number, enter it into both blanks.) (smaller number) (larger number)

Answer 1

Both the numbers are 8.

Explanation:

Let the two numbers are p and 64/p.

The sum is given by

`S = p +(64)/(p)\\\\(dS)/(dp)= 1 - (64)/(p^2)\\\\(dS)/(dp)=0\\\\(64)/(p^2)=1\\\\p= \pm 8`

So, the sum is minimum for p = 8 0r - 8, so the two numbers 8.