Chapter 8.3, Problem 47E

Profit. Suppose that profits on the sale of swimming suits are given approximately by

     $P\left(t\right)=5-5\cos \frac{\pi t}{26}0\le t\le 104$

where P(t) is profit (in hundreds of dollars) for a week of sales t weeks after January 1.

(A)    What is the rate of change of profit t weeks after the first of the year?

(B)    What is the rate of change of profit 8 weeks after the first of the year? 26 weeks after the first of the year? 50 weeks after the first of the year?

(C)    Find all local maxima and minima for 0 < t < 104.

(D)    Find the absolute maximum and minimum for 0 ≤ t ≤ 104.

(E)    Repeat part (C), using a graphing calculator.