MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
For a particular product, the daily revenue R (in thousands of dollars) depends on the selling price p (in dollars) according to
R(p)=p2e−0.02p,10≤p≤70.
Complete the tasks below.
(a) Derive an explicit expression for R′(p). Simplify your result.
(b) Evaluate R′(40) and include appropriate units.
(c) Interpret the meaning of the value obtained in part (b) for the company’s pricing strategy.
(d) Compute the average rate of change of R as p increases from 35 to 40 and compare it to the instantaneous rate from part (b). Explain the significance of any difference you observe.