Question: The income that a company receives from selling an item is called the revenue. Production decisions are based, in part, on how revenue changes if the quantity sold changes; that is, on the rate of change of revenue with respect to quantity sold. Suppose a company's revenue, in dollars, is given by R(q) = 100q - 10q2, where q is the quantity sold in kilograms.
(a) Calculate the average rate of change of R with respect to q over the intervals 1 ≤ q ≤ 2 and 2 ≤ q ≤ 3.
(b) By choosing small values for h, estimate the instantaneous rate of change of revenue with respect to change in quantity at q = 2 kilograms.