# Rate of Change Chapter Exam

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#### Question 1 1. How many zeroes does the derivative of this graph have?

#### Question 2 2. Which of the following is not a rate of change?

#### Question 3 3. According to Rolle's theorem, for a continuous function f(x), if the start point f(a) and the end point f(b) equal 0 then:

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Question 4
4.
According to the mean value theorem, at how many points will the instantaneous rate of change equal the average rate of change between *x* = 1 and *x* = 3 on the following graph?

#### Question 5 5. Which is greater, the derivative at a or the derivative at b?

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Question 6
6.
If the continuous function g(t) equals 5 at the points t=2 and t=4, then what can you say about g(t)?

A) Between t=2 and t=4 there will be at least one point where the instantaneous rate of change is 0.

B) Between t=2 and t=4 the average rate of change is 0.

C) Between t=2 and t=4, g(t) is constant.

#### Question 7 7. Where t= time, what is the derivative of f(t)?

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Question 8
8.
Which of the following are rates of change?

a) the acceleration of an object

b) the position of an object

c) the velocity of an object

#### Question 9 9. Where is f(x) differentiable?

#### Question 10 10. What is the rate of change at the point B in the graph below (for y in relation to x)?

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#### Question 11 11. Where is f(x) differentiable?

#### Question 12 12. Consider the function f(x) given below. According to Rolle's theorem, for how many values of x is the instantaneous rate of change equal to 0?

#### Question 13 13. If your average rate of change is 75 mph and you started at 0 mph, does it mean that you also drove faster than 75 mph at some point?

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Question 14
14.
What is the rate of change at the point B in the graph below (for y in relation to x)?

(In other words, what is the slope of the line from x = 2 to x = 3?)

#### Question 15 15. True or False: The slope of a curve is the tangent.

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#### Question 16 16. Does Rolle's theorem apply to this function?

#### Question 17 17. What is the rate of change at point A of the graph below.

#### Question 18 18. Will a function with 2 zeroes have an instantaneous rate of change of zero?

#### Question 19 19. Is this function differentiable over the region beginning at x=-2 and ending at x=2?

#### Question 20 20. At how many points on the graph below is the derivative of f(x)=0?

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#### Question 21 21. When you blow up a balloon, the time that it takes to blow it up depends on how much pressure the inlet air is under. (AKA, how hard you blow!) If the pressure is higher, the rate of change of the balloon volume _____ as a function of time.

#### Question 22 22. Velocity is a rate of change of _____.

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Question 23
23.
Which of the following statements are true?

a) d/dx f(x) = f'(x)

b) f'(x) is the derivative of the function f(x) with respect to x.

c) d/dx f(x) describes the instantaneous rate of change of f(x).

#### Question 24 24. Consider the graph below. Between x=C and x=-C, for any value of C, will there be a point where the instantaneous rate of change is 0?

#### Question 25 25. What is the rate of change at the point A in the graph below (for y in relation to x)?

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#### Question 26 26. Which point on the following graph satisfies the mean value theorem between x = 0 and x = 3?

#### Question 27 27. You start heading to your friend's house at 9:30 am starting from a standstill of 0 mph. You reach your friend's house at 9:50 am. Your friend only lives 10 miles away but the speed limit is so slow and there was so much traffic today that you drove a bit too fast during a small part of the trip. What is your average rate of change?

#### Question 28 28. What is the average rate of change for the interval with endpoints A and B?

#### Question 29 29. What does dy/dt mean?

#### Question 30 30. Consider the function f(x) given below. According to Rolle's theorem, between x=0 and x=pi, for how many values of x is the instantaneous rate of change equal to 0?

#### Rate of Change Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!