Chapter 8.2, Problem 4MP

Suppose that revenues from the sale of ski jackets are given approximately by

     $R\left(t\right)=6.2+5.8\cos \frac{\pi t}{6}0\le t\le 24$

where R(t) is revenue (in thousands of dollars) for a month of sales t months after January 1.

(A)    What is the rate of change of revenue t months after the first of the year?

(B)    What is the rate of change of revenue 2 months after the first of the year? 12 months after the first of the year? 23 months after the first of the year?

(C)    Find all local maxima and minima for 0 < t < 24.

(D)    Find the absolute maximum and minimum for 0 ≤ t ≤ 24.

(E)    Illustrate the results from parts (A)–(D) by sketching a graph of y = R(t) with the aid of a graphing calculator.