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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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 Spring '08
 CLARK,C.W./HOY,R.R

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