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.

Question

asked Feb 19, 2020 171k views

1 Answer

Glesage · Answer 1 · 2020-02-23T11:46:47+0000

Answer:

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