Question

Find two positive real numbers whose product is a maximum. (Enter your answers as a comma-separated list.) The sum of the first and twice the second is 16.

Answer 1

Explanation:

Let the first number be x and second number be y

`x+2y = 16`

Product =P(x) =
`xy =y(16-2y) = 16y-2y^2`

Use derivative test to find maxima for product

`P'(x) =16-4y\\P`

Equate I derivative to 0

`y =4`

Substitute to find x =
`16-2(4) =8`

Thus the two numbers are small one is 4 and big number is 8