Chapter 2, Problem 50RE

The water level in a reservoir varies during the year. Let $h\left(t\right)$ be the depth (in feet) of water at time $t$ days, where $t=0$ at the beginning of the year. Match each set of information about $h\left(t\right)$ and its derivative with the corresponding description of the reservoir’s activity.

Information:

A. $h\left(t\right)$ has the value $50$ for $1\le t\le 2$.

B. $h\text{'}\left(t\right)$ has the value $.5$ for $1\le t\le 2$.

C. $h\text{'}\left(t\right)$ is positive at $t=a$.

D. $h\text{'}\left(t\right)$ is negative at $t=a$.

E. $h\text{'}\left(t\right)$ and $h\text{'}\text{'}\left(t\right)$ are positive at $t=a$.

F. $h\text{'}\left(t\right)$ is positive and $h\text{'}\text{'}\left(t\right)$ is negative at $t=a$.

Descriptions:

a. The water level is rising at an increasing rate at time $a$.

b. The water level is receding at time $a$.

c. The water level is constant at $50$ feet on January $2$.

d. At time $a$ the water level is rising, but the rate of increase is slowing down.

e. On January $2$ the water rose steadily at a rate of $.5$ foot per day.

f. The water level is rising at time $a$.