I'm assuming you meant to type

So profit is sales-cost. Therefore,

To find the maximum, you must first differentiate giving you .

Then find the critical numbers by setting V'(x) to 0.

Quadratic formula gives you the critical values of x=98 and x=-94 but those aren't in the interval (0,9). So the maximum is when x is either 0 or 9. You can eliminate 0 because they would obviously make no profit if they didn't make a product. So plug x=9 into the profit equation.

The maximum profit is $251625