The product of two numbers is 28. What is the minimum value of their sum
The product of two numbers is equal to 28. If one of the numbers is represented by x, the value of the other number is `28/x` .
This gives the sum of the numbers as `S = x + 28/x` .
To determine the minimum value of the sum solve S' = 0 for x; also, the value of S'' for the particular solution of x should be positive.
`S' = 1 - 28/x^2`
`1 - 28/x^2 = 0`
=> `x^2 = 28`
=> `x = +-sqrt 28`
`S'' = 56/x^3`
This is positive for `x = sqrt 28`
The minimum value of the `2*sqrt 28`