Differentiable Functions & Min-Max Problems 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!

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Question 1 1. 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 2 2. What is the rate of change at the point A in the graph below (for y in relation to x)?

Question 3 3. What is the value of x at the finite local minimum for the function f(x) = 2x^3 - 3x^2?

Question 4 4. 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 5 5.

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?)

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Question 6 6. What is the average rate of change for the interval with endpoints A and B?

Question 7 7. Acceleration is the measure of how velocity changes over time. Acceleration is an example of _____.

Question 8 8. Which of the following is a local minimum?

Question 9 9. Where is the global maximum for the function y=f(x) below between x=0 and x=2?

Question 10 10. 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 11 11. What is the global minimum for the function f(x) = sin((pi)x) between x = 0 and x = 2?

Question 12 12. What is the approximate instantaneous rate of change at point C?

Question 13 13. What is the rate of change at the point B in the graph below (for y in relation to x)?

Question 14 14. Your friend walks 15 minutes from her house to the school every day. What is her walking speed, if her house is 0.5 miles from her school?

Question 15 15. 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 16 16. Where is the global minimum for the function f(x) = sin((pi)x) below between x=0 and x=2?

Question 17 17. 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 18 18. Which of the following BEST describes point B?

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

Question 20 20. Velocity is a rate of change of _____.

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Question 21 21. What is value of y at the finite local maximum for the function f(x) = 2x^3 - 3x^2?

Question 22 22. What is value of y at the finite local maximum for the function y=f(x) below?

Question 23 23. Over the region shown, the global minimum is at the point

Question 24 24. What is the global minimum for the function y=f(x) below between x=0 and x=2?

Question 25 25. What is the global minimum for the function y=f(x) below between x=0 and x=2?

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Question 26 26. When driving over mountains, the grade of the road tells drivers how steep the climb is going up or down the mountain. The grade is the rate of change of _____.

Question 27 27. Which of the following BEST describes point C?

Question 28 28. Which of the following BEST describes point A?

Question 29 29. Which point on the following graph satisfies the mean value theorem between x = 0 and x = 3?

Question 30 30. 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?

Differentiable Functions & Min-Max Problems 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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