AP Calculus BC : 4.1 Interpreting the Meaning of the  Derivative in Context- Exam Style questions with Answer- MCQ

Question

The rate at which water leaks from a tank, in gallons per hour, is modeled by R, a differentiable function of the number of hours after the leak is discovered. Which of the following is the best interpretation of R'(3)?

A The amount of water, in gallons, that has leaked out of the tank during the first three hours after the leak is discovered

B The amount of change, in gallons per hour, in the rate at which water is leaking during the three hours after the leak is discovered

C The rate at which water leaks from the tank, in gallons per hour, three hours after the leak is discovered

D The rate of change of the rate at which water leaks from the tank, in gallons per hour , three hours after the leak is discovered

Answer/Explanation

 

Question

A weight suspended by a spring vibrates vertically according to the function D given by \(D(t)=2\sin (4\pi (t+\frac{1}{8}))\), where D(t), in centimeters, is the directed distance of the weight from its central position t seconds after the start of the motion. Assume the positive direction is upward. What is the instantaneous rate of change of the weight’s position, in centimeters per second, at the moment the weight is first 1 centimeter above its central position?
A −157.914
B −21.765
C −12
D 0

Answer/Explanation

Ans:B

Question

A city planner developed the function P to model the population of a city over the next 25 years, where P(t) is the projected population of the city t years from now. According to the model, which of the following gives the rate at which the population of the city will be changing at time t=5 ?
A P(5)
B P(6)−P(4)
C \(\frac{P(5)}{5}\)
D P′(5)

Answer/Explanation

Ans:D

Question

The figure above shows the graph of the differentiable function f for 1≤x≤8 and the secant line through the points (1,f(1)) and (8,f(8)). For how many values of x in the closed interval [1,8] does the instantaneous rate of change of f at x equal the average rate of change of f over that interval?
A Zero
B Three
C Four
D Five

Answer/Explanation

Ans:C

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