1 - Missouri State University



|1. |Which graph represents[pic] if the graph of [pic]is displayed below? |

| |[pic] |

|A) |[pic] |D) |[pic] |

|B) |[pic] |E) |[pic] |

|C) |[pic] | | |

|2. |For the function in this problem, find the slope of the tangent line at the given value. |

| |[pic] |

| |A) 34 B) 26 C) 14 D) 0 E) 46 |

| | |

|3. |Find the slope of the tangent at [pic] |

| |[pic] |

| |A) –23 B) –4 C) –13 D) 4 E) 0 |

| | |

|4. |For the function in this problem, find the derivative, by using the definition. |

| |[pic] |

| |A) [pic] B) [pic] C) [pic] D) [pic] E) [pic] |

| | |

|5. |Find the slope of the tangent to the graph of f (x) at any point. |

| |[pic] |

| |A) [pic] B) [pic] C) [pic] D) [pic] E) [pic] |

| | |

|6. |Write the equation of the line tangent to the graph of f (x) at [pic] |

| |[pic] |

| |A) [pic]2[pic]3 B) [pic]2[pic]3 C) [pic]2[pic] D) [pic]2[pic]2 E) [pic]2[pic]2 |

| | |

|7. |Total cost Suppose the figure shows the total cost graph for a company. Arrange the average rates of change of total cost from A|

| |to B, B to C, and A to C from smallest to greatest. |

| |[pic] |

| |

| |

|A) |A to B then A to C then B to C |D) |A to C then B to C then A to B |

|B) |B to C then A to C then A to B |E) |A to C then A to B then B to C |

|C) |B to C then A to B then A to C | | |

|8. |Find the derivative of the function. |

| |[pic] |

|A) |[pic] |D) |[pic] |

|B) |[pic] |E) |[pic] |

|C) |[pic] | | |

| | |

|9. |Find the derivative of the function. |

| |[pic] |

|A) |[pic] |D) |[pic] |

|B) |[pic] |E) |[pic] |

|C) |[pic] | | |

| | |

|10. |Find the derivative of the function. |

| |[pic] |

|A) |[pic] |D) |[pic] |

|B) |[pic] |E) |[pic] |

|C) |[pic] | | |

| | |

|11. |At the indicated point, find the instantaneous rate of change of the function. |

| |[pic] |

| |A) –11 B) 42 C) 7 D) 9 E) –3 |

| |

|12. |Find the derivative at the given x-value. |

| |[pic] |

A) –9 B) –31 C) 9 D) –4.5 E) 0

|13. |Marginal revenue Suppose the total revenue function for a blender is [pic]where x is the number of units sold. What function |

| |gives the marginal revenue? |

|A) |[pic] |D) |[pic] |

|B) |[pic] |E) |[pic] |

|C) |[pic] | | |

| | |

|14. |Marginal revenue Suppose the total revenue function for a blender is [pic]where x is the number of units sold. What is the |

| |marginal revenue when [pic] units are sold, and what does it mean? |

|A) |34. Selling an additional unit when [pic] have been sold increases revenue by $34. |

|B) |4. Selling an additional unit when [pic] have been sold increases revenue by $4. |

|C) |64. Selling an additional unit when [pic] have been sold increases revenue by $64. |

|D) |34. Selling an additional unit when [pic] have been sold decreases revenue by $34. |

|E) |4. Selling an additional unit when [pic] have been sold decreases revenue by $4. |

| | |

|15. |For the function given, find all x-value(s) where[pic] |

| |[pic] |

| |A) [pic] B) [pic] C) [pic] D) [pic] E) [pic] |

| | |

|16. |Find [pic] if [pic]. |

|A) |[pic] |D) |[pic] |

|B) |[pic] |E) |[pic] |

|C) |[pic] | | |

| | |

|17. |Find the derivative of [pic]. |

| |A) [pic] B) [pic] C) [pic] D) [pic] E) [pic] |

| | |

|18. |Find the indicated derivative and simplify. |

| |[pic] for [pic] |

|A) |[pic] |D) |[pic] |

|B) |[pic] |E) |[pic] |

|C) |[pic] | | |

| | |

|19. |Find the indicated derivative and simplify. |

| |[pic] for [pic] |

|A) |[pic] |D) |[pic] |

|B) |[pic] |E) |[pic] |

|C) |[pic] | | |

| | |

|20. |Find the derivative of [pic]. |

| |A) 1 B) [pic] C) [pic] D) [pic] E) [pic] |

| | |

|21. |Find the third derivative. |

| |[pic][pic] |

| |A) [pic] B) [pic] C) [pic] D) [pic] E) 0 |

| | |

|22. |Find the third derivative. |

| |[pic] |

| |A) [pic] B) [pic] C) [pic] D) [pic] E) [pic] |

| | |

|23. |Acceleration If the formula describing the distance s (in feet) an object travels as a function of time t (in seconds) is [pic].|

| |What is the acceleration of the object when [pic] |

| |A) 0 ft/sec2 B) [pic] ft/sec2 C) [pic] ft/sec2 D) [pic] ft/sec2 E) [pic] ft/sec2 |

| | |

|24. |Find [pic] for the given function. |

| |[pic] |

|A) |[pic] |D) |[pic] |

|B) |[pic] |E) |[pic] |

|C) |[pic] | | |

| | |

|25. |Find the derivative of the given function. Simplify and express the answer using positive exponents only. |

| |[pic] |

|A) |[pic] |D) |[pic] |

|B) |[pic] |E) |[pic] |

|C) |[pic] | | |

| | |

|26. |Differentiate the given function. |

| |[pic] |

|A) |[pic] |D) |[pic] |

|B) |[pic] |E) |[pic] |

|C) |[pic] | | |

| | |

|27. |Pricing and sales A chain of auto service stations has found that its monthly sales volume y (in dollars) is related to the |

| |price p (in dollars) of an oil change according to [pic]. What is the rate of change of sales volume when the price is $60? |

| |Interpret your answer. |

|A) |–4815. If the price of an oil change goes from $60 to $61, the monthly sales volume will decrease by $4815. |

|B) |–140. If the price of an oil change goes from $60 to $61, the monthly sales volume will increase by $140. |

|C) |–140. If the price of an oil change goes from $60 to $61, the monthly sales volume will decrease by $140. |

|D) |–70. If the price of an oil change goes from $60 to $61, the monthly sales volume will decrease by $70. |

|E) |–70. If the price of an oil change goes from $60 to $61, the monthly sales volume will increase by $70. |

| | |

|28. |Budget deficit or surplus The table gives the yearly U.S. federal budget deficit (as a negative value) or surplus (as a positive|

| |value) in billions of dollars from 1990 to 2004. |

| | |

| |Year |

| |Deficit or Surplus |

| |Year |

| |Deficit or Surplus |

| | |

| |1990 |

| |[pic]221.2 |

| |1998 |

| |70.0 |

| | |

| |1991 |

| |[pic]269.4 |

| |1999 |

| |124.4 |

| | |

| |1992 |

| |[pic]290.4 |

| |2000 |

| |237.0 |

| | |

| |1993 |

| |[pic]255.0 |

| |2001 |

| |127.0 |

| | |

| |1994 |

| |[pic]203.1 |

| |2002 |

| |[pic]159.0 |

| | |

| |1995 |

| |[pic]164.0 |

| |2003 |

| |[pic]374.0 |

| | |

| |1996 |

| |[pic]107.5 |

| |2004 |

| |[pic]445.0 |

| | |

| |1997 |

| |[pic]22.0 |

| | |

| | |

| | |

| |Source: Budget of the United States Government |

| | |

| |Assume the federal budget deficit (or surplus) can be modeled with the function [pic], where D is in billions of dollars and t |

| |is the number of years past 1980. Use the model to find and interpret the instantaneous rate of change of the U.S. federal |

| |deficit (or surplus) in 1997. |

|A) |This model predicts a budget deficit increase of $361.2 billion from 1997 to 1998. |

|B) |This model predicts a budget deficit increase of $73.3 billion from 1997 to 1998. |

|C) |This model predicts a budget deficit decrease of $732.5 billion from 1997 to 1998. |

|D) |This model predicts a budget deficit decrease of $73.3 billion from 1997 to 1998. |

|E) |This model predicts a budget deficit decrease of $361.2 billion from 1997 to 1998. |

| | |

|29. |For the function displayed in the graph below, find all x-values at which the derivative does not exist. |

| |[pic] |

| |A) –2, 2 B) –4, 0, 4 C) 5 D) 0 E) 2 |

| | |

|30. |For the function displayed in the graph below, find all x-values at which the derivative does not exist. |

| |[pic] |

| |A) 2 B) 0, 3 C) none D) –1 E) –1, 3 |

| | |

|31. |Use the graph of [pic] to identify at which of the indicated points the derivative [pic] changes from positive to negative. |

| | |

| |[pic] |

| |A) (5,6) B) (-1,2) C) (2,4), (5,6) D) (-1,2), (5,6) E) (-1,2), (2,4) |

| | |

|32. |For the given function and graph, estimate the coordinates of the relative maxima by observing the graph, where [pic] |

| |[pic] |

| |[pic] |

| |A) [pic] B) [pic] C) [pic] D) [pic] E) no relative maxima |

| | |

|33. |For the given function and graph, determine all critical value(s), where [pic] |

| |[pic] |

| |[pic] |

|A) |[pic] |D) |[pic] |

|B) |[pic] |E) |[pic] |

|C) |[pic] | | |

| |

|34. |For the given function and graph, determine all critical point(s), where [pic] |

| |[pic] |

| |[pic] |

|A) |[pic] |D) |[pic] and [pic] |

|B) |[pic] |E) |[pic] and [pic] and [pic] |

|C) |[pic] | | |

| | |

|35. |Make a sign diagram for the function and determine all x-values at which relative maxima occur. |

| |[pic] |

| |A) [pic] B) [pic] C) [pic] D) [pic] E) no relative maxima |

| | |

|36. |Use the graph of [pic] to identify at which of the indicated points the derivative [pic] changes from negative to positive. |

| | |

| |[pic] |

| |A) (-1,2), (2,4) B) (-1,2) C) (2,4), (5,6) D) (5,6) E) (2,4) |

| | |

|37. |For the given function, find intervals of x-values where the function is decreasing. |

| |[pic] |

| |A) [pic] B) [pic] C) [pic] D) [pic] E) [pic] |

| | |

|38. |For the given function, find all intervals of x-values where the function is increasing. |

| |[pic] |

| |A) [pic] B) [pic] C) [pic] D) [pic] E) [pic] |

| | |

|39. |Both a function and its derivative are given. Use them to find the relative minima. |

| |[pic] |

|A) |[pic] |D) |[pic],[pic] |

|B) |[pic] |E) |no relative minima |

|C) |[pic] | | |

| | |

|40. |Medication The number of milligrams x of a medication in the bloodstream t hours after a dose is taken can be modeled by [pic] |

| |[pic]. For what t-values is x increasing? Round answers to two decimal places. |

| |A) [pic] B) [pic] C) [pic] D) [pic] E) [pic] |

| | |

|41. |A graph of [pic] is given. Use the graph to determine where f (x) is decreasing. |

| |[pic] |

| |[pic] |

| |A) [pic] B) [pic] C) [pic] D) [pic] E) [pic] |

| | |

|42. |A graph of [pic] is given. Use the graph to determine where the graph of [pic]has a relative maximum. |

| |[pic] |

| |[pic] |

| |A) [pic] B) [pic] C) [pic] D) [pic] E) no relative maxima |

| | |

|43. |For the function displayed in the graph below, which of the numbered points are inflection points? |

| |[pic] |

| |

| |

A) 2, 4, 5, 7 B) 1, 2, 3, 4, 6 C) 2, 4 D) 5, 7 E) 1, 3, 6

|44. |In this problem, [pic] and its graph are given. Use the graph of [pic] to determine where f (x) is concave down. |

| |[pic] |

| |[pic] |

| |A) [pic] B) [pic] C) [pic] D) [pic] E) [pic] |

| | |

|45. |Production Suppose that the total number of units produced by a worker in t hours of an 8-hour shift can be modeled by the |

| |production function [pic][pic]. Find the number of hours before production is maximized. |

| |A) [pic] B) [pic] C) [pic] D) [pic] E) [pic] |

| | |

|46. |For the given function and graph, estimate the coordinates of the relative maxima by observing the graph, where [pic] |

| |[pic] |

| |[pic] |

| |A) [pic] B) [pic] C) [pic] D) [pic] E) no relative maxima |

| | |

|47. |A function and its graph are given. From the graph, estimate where[pic]. |

| |[pic] |

| |[pic] |

| |A) [pic] B) [pic] C) [pic] D) [pic] E) [pic] |

| | |

|48. |In this problem, [pic] and its graph are given. Use the graph of [pic] to determine where f (x) is concave up. |

| |[pic] |

| |[pic] |

| |A) [pic] B) [pic] C) [pic] D) [pic] E) [pic] |

| | |

|49. |Use the graph shown in the figure and identify points from A through I that satisfy the given condition. |

| |[pic] |

| |[pic] |

| |A) C B) H C) G D) A E) D |

| | |

|50. |Find the absolute maximum for f(x) on the interval [a, b]. |

| |[pic] |

| |A) [pic] B) [pic] C) [pic] D) [pic] E) [pic] |

| | |

|51. |Find dy/dx for the following equation: |

| |[pic] |

|A) |[pic] |D) |[pic] |

|B) |[pic] |E) |[pic] |

|C) |[pic] | | |

| | |

|52. |Find dy/dx for the following equation: |

| |[pic] |

|A) |[pic] |D) |[pic] |

|B) |[pic] |E) |[pic] |

|C) |[pic] | | |

| | |

|53. |Find dy/dx for the following equation: |

| |[pic] |

|A) |[pic] |D) |[pic] |

|B) |[pic] |E) |[pic] |

|C) |[pic] | | |

| | |

|54. |Differentiate the given function. |

| | |

| |[pic] |

|A) |[pic] |D) |[pic] |

|B) |[pic] |E) |[pic] |

|C) |[pic] | | |

| | |

|55. |Differentiate the given function. |

| | |

| |[pic] |

|A) |[pic] |D) |[pic] |

|B) |[pic] |E) |[pic] |

|C) |[pic] | | |

| | |

|56. |Differentiate the given function. |

| | |

| |[pic] |

| |A) [pic] B) [pic] C) [pic] D) [pic] E) [pic] |

| | |

|57. |Differentiate the given function. |

| | |

| |[pic] |

|A) |[pic] |D) |[pic] |

|B) |[pic] |E) |[pic] |

|C) |[pic] | | |

| | |

|58. |Differentiate the given function. |

| | |

| |[pic] |

|A) |[pic] |D) |[pic] |

|B) |[pic] |E) |[pic] |

|C) |[pic] | | |

| | |

|59. |Differentiate the given function. |

| | |

| |[pic] |

| |A) [pic] B) [pic] C) [pic] D) [pic] E) 0 |

| | |

|60. |Differentiate the given function. |

| | |

| |[pic] |

|A) |[pic] |

|B) |[pic] |

|C) |[pic] |

|D) |[pic] |

|E) |[pic] |

| | |

|61. |Find the second derivative of the given function. |

| | |

| |[pic] |

|A) |[pic] |D) |[pic] |

|B) |[pic] |E) |[pic] |

|C) |[pic] | | |

| | |

|62. |Differentiate the given function. |

| | |

| |[pic] |

|A) |[pic] |D) |[pic] |

|B) |[pic] |E) |[pic] |

|C) |[pic] | | |

| | |

|63. |Differentiate the given function. |

| | |

| |[pic] |

|A) |[pic] |D) |[pic] |

|B) |[pic] |E) |[pic] |

|C) |[pic] | | |

| | |

ANSWERS

1. C 43. C

2. A 44. C

3. C 45. D

4. E 46. B

5. A 47. A

6. D 48. D

7. A 49. D

8. B 50. B

9. C 51. B

10. E 52. B

11. A 53. A

12. D 54. A

13. A 55. C

14. B 56. E

15. A 57. A

16. E 58. B

17. B 59. A

18. C 60. B

19. D 61. C

20. E 62. A

21. A 63. E

22. E

23. B

24. A

25. C

26. D

27. D

28. D

29. B

30. E

31. A

32. B

33. D

34. D

35. D

36. B

37. E

38. C

39. B

40. E

41. E

42. A

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