(x+3)³ 4(х — 1)2 12 16 f (x) Consider the function 11 + 4. Note that %3D 4 x - 1 (x – 1)2 (x – 9)(x + 3)² 4(x – 1)3 24(x + 3) (x – 1)ª . f'(x) f"(x) = and 1. Construct a table of signs for f'and f" which specifies the following: (a) the intervals on which the graph of f is increasing, decreasing, concave up, and concave down, and (b) the values of x at which f has relative extrema, inflection points, and vertical asymptotes (if any).
(x+3)³ 4(х — 1)2 12 16 f (x) Consider the function 11 + 4. Note that %3D 4 x - 1 (x – 1)2 (x – 9)(x + 3)² 4(x – 1)3 24(x + 3) (x – 1)ª . f'(x) f"(x) = and 1. Construct a table of signs for f'and f" which specifies the following: (a) the intervals on which the graph of f is increasing, decreasing, concave up, and concave down, and (b) the values of x at which f has relative extrema, inflection points, and vertical asymptotes (if any).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Please provide the table of signs for f' and f''.
Transcribed Image Text:(x+3)³
4(х — 1)2
12
16
f (x)
Consider the function
11
+
4. Note that
%3D
4
x - 1
(x – 1)2
(x – 9)(x + 3)²
4(x – 1)3
24(x + 3)
(x – 1)ª .
f'(x)
f"(x) =
and
1. Construct a table of signs for f'and f" which specifies the following:
(a) the intervals on which the graph of f is increasing, decreasing, concave up, and
concave down, and
(b) the values of x at which f has relative extrema, inflection points, and vertical
asymptotes (if any).
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