Use the following information for questions 1–3:
the rate at which water flows into a tank, in gallons per hour, is given by a differentiable function r of time t. the table below gives the rate as measured at various times in an 8-hour time period.
t (hours) 0 2 3 7 8
r(t) (gallons per hour) 1.95 2.5 2.8 4 4.26
2.) is there some time t, 0 < t < 8, such that r′(t) = 0? justify your answer.
3.) the rate of water flow r(t) can be estimated by w(t) = ln(t2 + 7). use w(t) to approximate the average rate of water flow during the 8-hour time period. indicate units of measure.