By William Ma

ISBN-10: 007137714X

ISBN-13: 9780071377140

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**Extra info for AP Calculus AB**

**Example text**

D) If region R is the base of a solid whose cross sections perpendicular to the x-axis are squares, find the volume of the solid. 4. The graph of f′, the derivative of the function f, for −4 ≤ x ≤ 6 is shown in Figure D-11. (a) At what value(s) of x does f have a relative maximum value? Justify your answer. (b) At what value(s) of x does f have a relative minimum value? Justify your answer. (c) At what value(s) of x does f″(x) > 0? Justify your answer. (d) At what value(s) of x, if any, does the graph of f have a point of inflection?

Figure DS-10 See Figure DS-9. The only graph that satisfies the behavior of g is choice (A) 85. From Chapter 9 See Figure DS-11. Figure DS-9 The graph indicates that the maximum acceleration occurs at the endpoint t = 6. a(t) = t2 − 4t and a(6) = 62 − 4(6) = 12 Figure DS-11 82. 506 gallons. 83. 06858. 657. sin 2x = 1 1 ⇒ 2x = sin −1 2 2 ⇒ 2x = 5π 5π π π ⇒ x = or 2x = or x = 6 6 12 12 86. 503 1 1 k 5730 Thus, y0 = y0e ( ) ⇒ = e 5730k 2 2 1 1 ln = ln(e 5730k ) ⇒ ln = 5730k 2 2 2 2 89.

Evaluate ∫ sin(2t ) dt. x π 28. If a function f is continuous for all values of x, which of the following statements is always true? I. ∫ f ( x)dx = ∫ f ( x)dx + ∫ f ( x)dx II. ∫ f ( x)dx = ∫ f ( x)dx − ∫ f ( x)dx III. ∫ f ( x)dx = ∫ f ( x)dx − ∫ f ( x)dx c a b a c b b c a b c b a c a b a c 0267-02/Part II 12/18/2001 17:24 Page 21 What You Need to Know About the AP Calculus AB Exam • (A) (B) y x 0 0 x 0 y (D) (C) y x 0 x Figure D-5 y f 0 10 Figure D-6 y 0 y (E) x 21 x 0267-02/Part II 12/18/2001 17:24 Page 22 22 • What You Need to Know About the AP Calculus AB Exam Section I—Part B Number of Questions Time Use of Calculator 17 50 Minutes Yes Directions: Use the same answer sheet as for Part A.

### AP Calculus AB by William Ma

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