Chapter 8.3, Problem 50E

Pollution. In a large city, the amount of sulfur dioxide pollutant released into the atmosphere due to the burning of coal and oil for heating purposes varies seasonally. Suppose that the number of tons of pollutant released into the atmosphere during the nth week after January 1 is given approximately by

      $P(n)=1+\cos \frac{\pi n}{26}0\le n\le 104$

(A)    What is the rate of change of pollutant n weeks after the first of the year?

(B)    What is the rate of change of pollutant 13 weeks after the first of the year? 26 weeks after the first of the year? 30 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 $\le$ t $\le$ 104.

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