1. Consider the function f(x) = r+1+ Note that r -4 1² – 4 r*(r² – 12) f'(x) 82(r² + 12) (1* – 4)ª and f"(x) = (2² – 4)² and the z-intercept of the graph of f is approximately z a 1.3146. (a) Evaluate all the necessary limits to identify all the linear asymptotes of the graph of f. (b) Construct a table of signs for f' and f" that specifies the following: i. the intervals on which the graph of f is increasing, decreasing, concave up, and concave down, and ii. the values of z at which f has relative extrema, inflection points, and vertical asymptotes (if any). (c) Sketch the graph of ƒ with emphasis on concavity. Label all the intercept points, relative extremum points, inflection points, and holes (if any) with their coordinates. Show the asymptotes of the graph of f and label them with their respective equa-
1. Consider the function f(x) = r+1+ Note that r -4 1² – 4 r*(r² – 12) f'(x) 82(r² + 12) (1* – 4)ª and f"(x) = (2² – 4)² and the z-intercept of the graph of f is approximately z a 1.3146. (a) Evaluate all the necessary limits to identify all the linear asymptotes of the graph of f. (b) Construct a table of signs for f' and f" that specifies the following: i. the intervals on which the graph of f is increasing, decreasing, concave up, and concave down, and ii. the values of z at which f has relative extrema, inflection points, and vertical asymptotes (if any). (c) Sketch the graph of ƒ with emphasis on concavity. Label all the intercept points, relative extremum points, inflection points, and holes (if any) with their coordinates. Show the asymptotes of the graph of f and label them with their respective equa-
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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Transcribed Image Text:13 + x? – 4
2 - 4
4x
= I+1+
1. Consider the function f(r)
Note that
12 - 4
x*(r² – 12)
(2² – 4)?
82(x? + 12)
(x² – 4)3
f'(x)
and f"(x) =
and the x-intercept of the graph of f is approximately zz 1.3146.
(a) Evaluate all the necessary limits to identify all the linear asymptotes of the graph
of f.
(b) Construct a table of signs for f' and f" that specifies the following:
i. the intervals on which the graph of f is increasing, decreasing, concave up, and
concave down, and
ii. the values of z at which f has relative extrema, inflection points, and vertical
asymptotes (if any).
(c) Sketch the graph of f with emphasis on concavity. Label all the intercept points,
relative extremum points, inflection points, and holes (if any) with their coordinates.
Show the asymptotes of the graph of f and label them with their respective equa-
tions.
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