Question

Find two positive numbers whose sum is 16 and the sum of cubes of them is minimum.

Answer 1

Answer:

https://www.teachoo.com/4411/712/Ex-6.5--16---Find-two-positive-numbers-whose-sum-is-16/category/Ex-6.5/

Step-by-step explanation:

Answer 2

Two numbers are 8 and 8.

Step-by-step explanation:

Let's assume that the two numbers are x and y

Given that x + y = 16, we get y = 16 - x

Sum S = x^2 + y^2

          = x^2 + (16-x)^2

          = x^2 + 256 + x^2 - 32x

          = 2x^2 - 32x + 256

dS/dx = 4x - 32

For the sum to be minimum, dS/dx = 0

4x - 32 = 0

4x = 32

x = 8

y = 16-x

Substituting the x value we just found, we get y = 16-8 = 8

So, the two numbers are 8 and 8.