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The Derivative as a Function 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. 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 2 2. What is the approximate instantaneous rate of change at point C?

Question 3 3. What is the average rate of change for the interval with endpoints A and B?

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. 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?

Page 2

Question 6 6. The derivative of the following graph is _____ at point A.

Question 7 7. The derivative of the following graph is _____ at point D.

Question 8 8. 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 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. 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?

Page 3

Question 11 11. Which point on the following graph satisfies the mean value theorem between x = 0 and x = 3?

Question 12 12. If a function's derivative is positive at point a, then what do we know about the function?

Question 13 13. The derivative of the following graph is _____ at point C.

Question 14 14. 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?

Question 15 15. Which could be the graph of the derivative of the function below?

The Derivative as a Function 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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