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

Answer:

Both the numbers are 8.

Step-by-step explanation:

Let the two numbers are p and 64/p.

The sum is given by

$S = p +\frac{64}{p}\\\\\frac{dS}{dp}= 1 - \frac{64}{p^2}\\\\\frac{dS}{dp}=0\\\\\frac{64}{p^2}=1\\\\p= \pm 8$

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