**The sum of two numbers is 15. What are these numbers if their product is as large as possible.**

Let x, y be the numbers

Thus x + y = 15

x y = p*(Their product)*

\(P = x(15-x)\)

\(P = 15x-x^2\)

\(\frac{dP}{dx} = 15-2x\)

\(0 = 15-2x\)

\(x = 7.5\)

\(y = 7.5\)

*Thus the numbers are:*

\(x = 7.5\)

\(y = 7.5\)