Chapter 9.8, Problem 42E

Advertising and sales A product with a large advertising budget has its sales S (in millions of dollars) given by

$s=\frac{500}{t+2}-\frac{1000}{{(t+2)}^2}$ where t is the number of months the product has been on the market.

(a) Find the rate of change of sales at any time t.

(b) What is the rate of change of sales at t = 2?

(c) Use the second derivative to find how this rate is changing at t = 2.

(d) Interpret your results from parts (b) and (c).