Question

Help find answer 18?

Answer 1

`5`

Explanation:

let `x=`one of the positive integers
that means `10-x` is the other positive integer since they add to 10.

the product of those numbers is `x(10-x) = -x^2+10x`
you want to maximize the value `-x^2+10x`

this graph is a parabola opening down, as you can see from the -1 coefficient on the `x^2` term.

the maximum value of `-x^2+10x` occurs at the vertex, or where the derivative = 0.

`d/dx(-x^2+10x)=-2x+10`
`-2x+10=0` when `x=5`

this means the vertex of the graph is `(5,25)`, meaning the two positive integers are 5 and 10-5, or simply 5 and 5.

the answer is `5`.