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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