For time 0

For tme() < t 10, water IS flowing into a small tub at a ratc given by the function F defined by ) _ For time 5 < t < 1(). water is leaking from the tub at a rate given by the function L arctan 75). Both F (t) and L (t) are measured in cubic feet per minute, and t is defined by L (t) = 0.03 measured in minutes. The volume of water in the tub, in cubic feet, at time t minutes is given by II' (t). 3, there are 2.5 cubic feet of water in the tub. Write an equation for the locally linear (a) At time t approximation of 11' at interpret the mqanina of (8) in the context of the problem. (c) Is there a time t, for 5 < < 10, at which the rate of change of the volume of water in the tub changes from positive to ne ative? Give a reas o o nswer.. (d) The tub is in the shape of a 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 = C)