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Graphing Derivatives and L'Hopital's Rule 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.

According to L'Hopital's rule, which of the following statements MUST be true for the equation shown below to hold?

A) f(x) and g(x) approach 0 or infinity

B) f'(C) does not equal 0

C) g'(x) does not equal 0

Question 2 2. Consider the function h(x) below. At x = 1 is this function concave up, concave down, or an inflection point?

Question 3 3. What is the global minimum of a function?

Question 4 4. If a function's derivative is positive at point a, then what do we know about the function?

Question 5 5. Consider the function r(s) below. At s = 1 is this function concave up, concave down, or an inflection point?

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Question 6 6. The graph shown is an example of a function that:

Question 7 7. Does L'Hopital's rule apply to this problem? Why or why not?

Question 8 8. What is value of y at the finite local maximum for the function y=f(x) below?

Question 9 9. Find the following limit:

Question 10 10. Consider the function f(x) below. At x = 2 is this function concave up, concave down, or an inflection point?

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Question 11 11. If ƒ ″(x) = 0, then f(x) will be a quadratic.

Question 12 12. Find the following limit:

Question 13 13. Evaluate the limit shown below:

Question 14 14. Which of the following BEST describes point C?

Question 15 15. At what points are extrema found?

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Question 16 16. Use L'Hopital's rule to find the limit.

Question 17 17. Given the graph of f'(x) below, what can you say about f(x)?

Question 18 18. If the second derivative of a function is positive, what does that tell you about the function?

Question 19 19. True or false: Every point where the second derivative of the function equals 0 is an inflection point.

Question 20 20. An inflection point occurs when the function . . .

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Question 21 21. What is the global minimum for the function y=f(x) below between x=0 and x=2?

Question 22 22. If the derivative of a function is a rising concave up, what does that mean for the function?

Question 23 23. What is the limit of the following:

Question 24 24. What is the equation of the line tangent to f(x) at the point x=0?

Question 25 25. Which of the following must be true before you can apply L'Hopital's rule?

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Question 26 26. What is the slope of a line normal to f(x)?

Question 27 27. Evaluate the limit of the following:

Question 28 28. Can a continuous function have a point where the derivative is not continuous?

Question 29 29. Where is the global maximum for the function y=f(x) below between x=0 and x=2?

Question 30 30. A straight line function will yield what type of derivative?

Graphing Derivatives and L'Hopital's Rule 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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