1. (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 r. 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(r)dr. Using correct units, explain the meaning of your answer in terms of water flow. (b) Is there some time 1, 0 < < 24, such that R'(t)=0? Justify your answer.