Question

find two positive numbers whose sum is 17 and whose product is a maximum.

Answer 1

The numbers are x and 17-x

The product gives us:
f(x)=x(17-x) = -x^2+17x

To find the maximum you have to take the derivative of the function (-x^2+17x) and then solve it for zero.

d/dx=-2x+17

d/dx=0 gives us -2x+17=0
x=17/2 <==> x=8.5

If you need the point of the maximum you insert x into f(x)=x(17-x) and get:
f(x)=72.25

Hope this helps!

//Ali

Answer 2

very much so thanks