Find the minimum product of two numbers whose difference is nine.

The minimum product of two numbers has to be determined where the difference of the numbers is 9.

If one of the numbers is represented by x, the other number is x - 9.

The product of the two numbers is x*(x - 9) = x^2 - 9x

Now if we plot y = x^2 - 9x we get the following graph:

Take the derivative of y = x^2 - 9x

dy/dx = 2x - 9

equate this to 0 and solve for x

2x - 9 = 0

x = 4.5

At x = 4.5, y = (4.5)^2 - 9*(4.5) = -20.25

The minimum value of the product is -20.25