(t) (hours) R(t) (gallons per hour)0 9.63 10.4 6 10.89 11.212 11.415 11.318 10.721 10.224 9.6The 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 ??? 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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