1. The quantity, q, of a certain hoverboard sold depends on the selling price, p, in dollars, so we write q = f(p). You are given that
f(140) = 13,000 and f'(140) = -100.
a. What does f'(140) = -100 tell you about the sales of hoverboards? Why is it reasonable that it is negative?
b. Briefly explain why the total revenue, R earned by the sale of skateboards is given by the formula R = pq.
c. From (b), since q is a function of p, the revenue R(p) is as well. Find R'(p), and explain each of the two terms in the formula in
terms of revenues, prices, and hoverboards. (Each term has its own intuitive reasonability in terms of the context, and you should
be explaining it.)
d. Find R'(140), and then estimate the revenue if the price is dropped to $139.