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{"ops":[{"insert":"1) Find a point c satisfying the conclusion of the Mean Value Theorem for the function f(x)=x^\u22127 on the interval [1,7]."},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"2)a)Consider the function f(x)=2x^3\u221212x^2\u221230x+5 on the interval [\u22124,8]. Find the average or mean slope of the function on this interval."},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":" b)By the Mean Value Theorem, we know there exists at least one c in the open interval (\u22124,8) such that f\u2032(c) is equal to this mean slope. Find all values of c that work and list them. If there are no values of c , enter None."},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"3)Gravel is being dumped from a conveyor belt at a rate of 10 ft^3\/min. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing when the pile is 19 ft high?"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"4)At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 18 knots and ship B is sailing north at 19 knots. How fast (in knots) is the distance between the ships changing at 4 PM?"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"The distance is changing at "},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"}]}

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