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NES Math: Rate of Change Chapter Exam

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!

Page 1

Question 1 1. Where is y differentiable?

Question 2 2. 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 3 3. 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 4 4. What is the derivative of the following?

Question 5 5. The derivative of f(x) is equal to 0 at how many points on the graph below?

Page 2

Question 6 6. At how many points on the graph below is the derivative of f(x)=0?

Question 7 7. According to the mean value theorem, which of the following is true for a function f(x) that is continuous and differentiable between the points A and B?

Question 8 8. What is the value of f(x) at the red circle?

Question 9 9.

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

Page 3

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

Question 12 12. Where t= time, what is the derivative of f(t)?

Question 13 13.

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

Question 15 15. 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?

Page 4

Question 16 16. What is the rate of change at the point E in the graph below (for y in relation to x)?

Question 17 17. Consider the graph and question below..

Question 18 18. What is the rate of change at the point A in the graph below (for y in relation to x)?

Question 19 19. What is the rate of change at the point A in the graph below (for y in relation to x)?

Question 20 20. Where is f(x) differentiable?

Page 5

Question 21 21.

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

Question 23 23. Where is f(x) differentiable?

Question 24 24. 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 25 25. Where is f(x) differentiable?

Page 6

Question 26 26. 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:

Question 27 27.

Which of the following best describe(s) the derivative of a function?

a) It is the instantaneous rate of change.

b) It is the slope between any two points.

c) It is the tangent to the function.

Question 28 28.

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 29 29. Which is greater, the derivative at a or the derivative at b?

Question 30 30. What is the approximate instantaneous rate of change at point C?

NES Math: 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!

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