This is correct.

No. We are looking for what value(s) of

make

zero. You have found that there are two values for which this occurs:

and

. Both of these are break-even points. The first solution is the minimum amount of money that must be spent on advertising in order to turn a profit, and the second solution is the maximum amount of money that can be spent on advertising before the advertising costs outweigh the increased revenue.

Finding the midpoint of these two values actually gives you the x-coordinate of the

*vertex* of this parabola, which in this problem represents the amount of money that must be spent to get the

*maximum profit*.