Chapter 3.6, Problem 60E

Spring runoff The flow of a small stream is monitored for 90 days between May 1 and August 1. The total water that flows past a gauging station is given by

$V(t)=\{\begin{array}{ll}\frac{4}{5}{t}^2\hfill & \text{if}0\le t<45\hfill \\ -\frac{4}{5}(t^2-180t+4050)\hfill & \text{if}45\le t<90,\hfill \end{array}$

where V is measured in cubic feet and t is measured in days, with t = 0 corresponding to May 1.

1. a. Graph the volume function.
2. b. Find the flow rate function V′(t) and graph it. What are the units of the flow rate?
3. c. Describe the flow of the stream over the 3-month period. Specifically, when is the flow rate a maximum?