(t) (hours) R(t) (gallons per hour) 0 9.6 3 10.4 6

Question

(t) (hours)       R(t) (gallons per hour)
0                         9.6
3                        10.4 
6                        10.8
9                        11.2
12                      11.4
15                      11.3
18                      10.7
21                      10.2
24                        9.6
The rate at which water flows out of a pipe, in gallons per hour, is given by a differentiable function R of time 1. The table above shows the rate as measured every 3 hours for a 24-hour period.
(a) Use a midpoint Riemann sum with 4 subdivisions of equal length to approximate ∫₀²⁴ R(e)dt. Using correct units, explain the meaning of your answer in terms of water flow,

(b) Is there some time 1, 0 < 1< 24, such that R'(t) = 0 ? Justify your answer.

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