[FONT='Cambria','serif']There are 2 positive numbers who have a sum of 9. Determine the maximum value of the product of one number and the square of the other number.[/FONT]

Results 1 to 4 of 4

- Jun 15th 2008, 06:49 AM #1

- Joined
- Apr 2008
- Posts
- 48

- Jun 15th 2008, 06:58 AM #2

- Jun 15th 2008, 06:58 AM #3

- Jun 15th 2008, 07:00 AM #4
let be one of the numbers. so the other can be represented as

Let be the function representing the product as stated WLOG:

so, and we want the maximum, thus we need such that

therefore, either or but note that x is a positive number, therefore we take .

-----------------

optional: if , then we are sure that gives the maximum value for

and at , we have .