Chapter 3.5, Problem 25P

To determine

(a)

To graph:

The function $N=f\left(t\right)=19+9\cos \left(\frac{\pi }{6}t\right)$ for $0\le t\le 24$ and also check whether $f^{\prime }\left(1\right)$ and $f^{\prime }\left(10\right)$ are positive or negative.

To determine

(b)

To find:

The derivative of the below function where N is the number of bird species found in an Ohio forest:

$N=f\left(t\right)=19+9\cos \left(\frac{\pi }{6}t\right).$

To determine

(c)

To find:

$f\left(1\right),f^{\prime }\left(1\right),f\left(10\right)\text{and }{f}^{\prime }\left(10\right)$ and also give interpretation of these terms.