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

Information

A. h(t) has the value 50 for 1 ≤ t ≤ 2.

B. h′(t) has the value .5 for 1 ≤ t ≤ 2.

C. h′(t) is positive at t = a.

D. h′(t) is negative at t = a.

E. h′(t) and h(t) are positive at t = a. 

F. h′(t) is positive and h(t) 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.