Question

the sum of two nonnegative numbers is 36 find the numbers if

Answer 1

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,

 

Hope this helps for your other problem which requires the same basic method.