Exam2_3 8 - Version 208 – Exam 2 – Radin – (58305) B....

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Unformatted text preview: Version 208 – Exam 2 – Radin – (58305) B. 3 , 4 −∞, 2. −1, − 3. −∞, −1 , 4. 3 − ,1 4 5. −∞, − 1, ∞ f has exactly 1 local maximum, C. is concave up. 1. f has exactly 3 inflection points. 1. C only 3 4 2. B and C only 3 − ,∞ 4 3. A and C only 3 , 4 1, ∞ correct Explanation: The function f will be concave up when ′′ f (x) > 0, i.e., on the solution set of the inequality f ′′ (x) = 8x2 − 2x − 6 = 2(4x + 3)(x − 1) > 0. Thus f will be concave up on 3 −∞, − , 4 017 1, ∞ . 10.0 points 6. A only 7. B only Explanation: B. True: f has a local maximum at x = 1, but a local minimum at x = −2; since f ′ (x) < 0 immediately to the left and right of x = −3, f does not have a local maximum at x = −3. C. True: the graph changes concavity at (−3, 1) and at (−2, −1) as well at (−1, 1). 2 −2 5. none of them A. True: the graph of f is decreasing on (1, 3). 4 −4 4. A and B only 8. all of them correct If f is a continuous function on (−5, 3) whose graph is 2 keywords: reflection point, local maximum, True/False 018 which of the following properties are satisfied? A. ′ 8 f (x) < 0 on (1, 3), 10.0 points The figure below shows the graphs of three functions: ...
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