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:
\(x = 7.5\)
\(y = 7.5\)