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

Answer:

Step-by-step 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

$P'(x) =16-4y\\P"=-4$

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