Im trying to help a friend with a business calculus problem but it has been about 7 years since i have taken any kind of math class and am drawing a blank. Could anyone help me out here so I can explain this to my friend?

You are a book publisher and in order to sell "q" thousand new novels each month, the price "p" must be sqrt(1152-4q^2) dollars. How many novels must be sold each month to maximize your revenue and what must the price of each novel at that sales level be?

I know this is a pretty simple take the derivative and find the max kind of problem but its been so long I'm having trouble remembering where to get started on this. Any help will be appreciated. Thanks!

About all I get out of that is - the lower the price the more will be sold, until you get so low you arn't making any money to start with.

The "trick" to the problem is to recognize that you are trying to maximize revenue (r), not the number of books sold. You do not have an equation for revenue, but we know that the revenue is equal to the price times the quantity: r = p * q

Hence, since:

r = p * q
r = q * (sqrt(1152-4q^2))

To find the maxima, you set the first derivative to zero and solve (dr/dq = 0 and solve for q). That tells you the q that maximizes the revenue. Then substitute the maxima q back into the price formula and you have your price.

Edit: I left out a ). Let me know if you want the answer so your buddy can check his work.