Answer to Question #260687 in Math for Stormer

Question

1) Find a point c satisfying the conclusion of the Mean Value Theorem for the function f(x)=x^−7 on the interval [1,7].

2)a)Consider the function f(x)=2x^3−12x^2−30x+5 on the interval [−4,8]. Find the average or mean slope of the function on this interval.

b)By the Mean Value Theorem, we know there exists at least one c in the open interval (−4,8) such that f′(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.

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?

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?

The distance is changing at

Answer 1

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