The Figure Above Shows the Graph of a Continuous Function F X Which Has Horizontal

Questions and Worked Solutions for AP Calculus AB Multiple Choice 2008 (Part B).

AP Calculus AB Multiple Choice 2008 Questions - Complete Paper (pdf)

AP Calculus AB Multiple Choice 2008 Question 76
76. The graph of f', the derivative f, is shown above for -2 ≤ x ≤ 5. On what intervals is f increasing?

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AP Calculus AB Multiple Choice 2008 Question 77
77. The figure above shows the graph of a function f with domain 0 ≤ x ≤ 4. Which of the following statements are true?

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AP Calculus AB Multiple Choice 2008 Question 78
78. The first derivative of the function f is defined by f'(x) = sin(x³ - x) for 0 ≤ x ≤ 2. On what interval(s) is f increasing?

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AP Calculus AB Multiple Choice 2008 Question 79

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AP Calculus AB Multiple Choice 2008 Question 80
80. The derivative of the function f is given by f'(x) = x²cos(x²). How many points of inflection does the graph of f have on the open interval (−2, 2 ?)

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AP Calculus AB Multiple Choice 2008 Question 81
81. If G(x) is an antiderivative for f(x) and G(2) = -7, then G(4) =

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AP Calculus AB Multiple Choice 2008 Question 82
82. A particle moves along a straight line with velocity given by v(t) = 7 - (1.01)^-t2 at time t ≥ 0. What is the acceleration of the particle at time t = 3?

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AP Calculus AB Multiple Choice 2008 Question 83
83. What is the area enclosed by the curves y = x³ - 8x² + 18x - 5 and y = x + 5?

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AP Calculus AB Multiple Choice 2008 Question 84
84. The graph of the derivative of a function f is shown in the figure above. The graph has horizontal tangent lines at x = −1, x = 1, and x = 3. At which of the following values of x does f have a relative maximum?

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AP Calculus AB Multiple Choice 2008 Question 85
85. The table above gives values of a function f and its derivative at selected values of x. If f ' is continuous on the interval [-4, -1], what is the value of ∫f'(x)dx?

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AP Calculus AB Multiple Choice 2008 Question 86
86. The table gives selected values of the velocity, v(t), of a particle moving along the x-axis. At time t = 0, the particle is at the origin. Which of the following could be the graph of the position, x(t), of the particle for 0 ≤ t ≤ 4?

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AP Calculus AB Multiple Choice 2008 Question 87
87. An object traveling in a straight line has position x(t) at time t. If the initial position is x(0) = 2 and the velocity of the object is v(t) = 3√(1 + t²), what is the position of the object at time t = 3?

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AP Calculus AB Multiple Choice 2008 Question 88
88. The radius of a sphere is decreasing at a rate of 2 centimeters per second. At the instant when the radius of the sphere is 3 centimeters, what is the rate of change, in square centimeters per second, of the surface area of the sphere? (The surface area S of a sphere with radius r is S = 4πr²)

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AP Calculus AB Multiple Choice 2008 Question 89
89. The function f is continuous for -2 ≤ x ≤ 2 and f(-2) = f(2) = 0. If there is no c, where -2 < c < 2, for which f'(c) = 0, which of the following statements must be true?

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AP Calculus AB Multiple Choice 2008 Question 90
90. The function f is continuous on the closed interval [2, 4] and twice differentiable on the open interval (2, 4). If f'(3) = 2 and f"(3) < 0 on the open interval (2, 4), which of the following could be a table of values for f?

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AP Calculus AB Multiple Choice 2008 Question 91
91. What is the average value of y = cos x/(x² + x + 2) on the closed interval [1, 3]?

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AP Calculus AB Multiple Choice 2008 Question 92
92. A city located beside a river has a rectangular boundary as shown in the figure above. The population density of the city at any point along a strip x miles from the river's edge is f(x) persons per square mile. Which of the following expressions gives the population of the city?

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