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cu ator 2. For time O t S 10, water is flowing into a small tub at a rate given by the function F defined by F(t) arctan For time 5 t 10, water is leaking from the tub at a rate given by the 2 10 function L defined by L(t) = 0.03(20t 75). Both F(t) and L(t) are measured in cubic feet per minute, and t is measured in minutes. 'Ihe volume of water in the tub, in cubic feet, at time t minutes is given by W(t). a. At time t = 3, there are 5.5 cubic feet of water in the tub. Write an equation for the linear approximation of Wat t = 3, and use it to approximate the volume of water in the tub at time t = 3.5. b. Find W' '(6). Using correct units, interpret the meaning of W" (6) in the context of the problem. c. Is there a time t, for 5 < t < 10, at which the rate of change of the volume of watefinthetub changes from positive to negative? Justify. d. The tub is in the shape ofa rectangular box that is 0.5 foot wide, 4 feet long, and 3 feet deep. What is the rate of change of the depth of the water in the tub at time t = 6?