Find two positive numbers whose product is 36 and whose sum is a minimum.

Let one of the numbers be x. The other number cab then be represented as 36-x (x+36-x = 36).

The product can then be represented as y = x (36-x) or y=36x-x2

The maximum or minimum is always on the axis of symmetry which has the formula x=-b/2a.

In our case, the axis of symmetry is - 36/-2, so x=18.

If one number is 18 and the 2 numbers add to 36, the other number is 18 as well.

So the 2 numbers are 18 and 18 and the maximum product is 324,