Iif F is Continuous for a x b and Differentiable Fo a x b Which of the Following Could Be False

Questions and Worked Solutions for AP Calculus AB Multiple Choice 1998

AP Calculus AB Multiple Choice 1969 - 1998 Questions - Complete Paper (pdf)

AP Calculus AB Multiple Choice 1998 Questions 1 - 5

1. What is the x-coordinate of the point of inflection on the graph of y = 1/3 x³ + 5x² + 24?

2. The graph of a piecewise-linear function f , for −1 ≤ x ≤ 4, is shown above. What is the value of

3. If f is continuous for a ≤ x ≤ b and differentiable for a < x < b , which of the following could be false?

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AP Calculus AB Multiple Choice 1998 Questions 6 - 10
6. If x² + xy = 10, then when x = 2, dy/dx =

8. Let f and g be differentiable functions with the following properties:
   (i) g(x) > 0 for all x
   (ii) f(0) = 1
   If h(x) = f(x)g(x) and h'(x) = f(x)g')x) then f(x) =

9. The flow of oil, in barrels per hour, through a pipeline on July 9 is given by the graph shown above. Of the following, which best approximates the total number of barrels of oil that passed through the pipeline that day?

10. What is the instantaneous rate of change at x = 2 of the function f given by f(x) = (x² - 2)/(x - 1)?

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AP Calculus AB Multiple Choice 1998 Questions 11 - 15
11. If f is a linear function and 0 0 < a < b, then

13. The graph of the function f shown in the figure above has a vertical tangent at the point (2,0) and horizontal tangents at the points (1, -1) and (3,1). For what values of x, -2 < x < 4, is f not differentiable?

14. A particle moves along the x-axis so that its position at time t is given by x(t) = t² - 6t + 5. For what value of t is the velocity of the particle zero?

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AP Calculus AB Multiple Choice 1998 Questions 16 - 20
16. If f(x) = sin(e^-x), then f'(x) =

17. The graph of a twice-differentiable function f is shown in the figure above. Which of the following is true?

18. An equation of the line tangent to the graph of y = x + cos x at the point (0,1) is

19. If f"(x) = x(x +1)(x - 2)², then the graph of f has inflection points when x =

20. What are all values of k for which

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AP Calculus AB Multiple Choice 1998 Questions 21 - 25
21. If dy/dt = ky and k is a nonzero constant, then y could be

22. The function f is given by f(x) = x⁴ + x² - 2. On which of the following intervals is f increasing?

23. The graph of f is shown in the figure above. Which of the following could be the graph of the derivative of f ?

24. The maximum acceleration attained on the interval 0 ≤ t ≤ 3 by the particle whose velocity is given by v(t) = t³ - 3t² + 12t + 4 is

25. What is the area of the region between the graphs of y = xt² and y = -x from x = 0 to x = 2?

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AP Calculus AB Multiple Choice 1998 Questions 26 - 28
26. The function f is continuous on the closed interval [0, 2] and has values that are given in the table above. The equation f(x) = 1/2 must have at least two solutions in the interval [0, 2] if k =

27. What is the average value of y = x²√(x³ + 1) on the interval [0, 2] ?

28. If f(x) = tan(2x), then f'(π/6) =

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