Give equations of the three linear asymptotes of the graph of f. b. Determine the intervals where ƒ is increasing or decreasing and where ƒ is concave up or concave down. Identify the relative extremum points and points of inflection, if there are any. a. c. Sketch the graph of f with emphasis on concavity. Label all the intercept points, relative extremum points, and inflection points with their respective coordinates, and the asymptotes with their respective equations.
Give equations of the three linear asymptotes of the graph of f. b. Determine the intervals where ƒ is increasing or decreasing and where ƒ is concave up or concave down. Identify the relative extremum points and points of inflection, if there are any. a. c. Sketch the graph of f with emphasis on concavity. Label all the intercept points, relative extremum points, and inflection points with their respective coordinates, and the asymptotes with their respective equations.
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
Transcribed Image Text:2. Consider the function f that satisfies the following:
• f is continuous everywhere except at x = -1,2,
f has an x-intercept at x = 1,
f has a y-intercept at y = -1,
lim f(x) = -∞ = lim f(x), lim f(x) = +∞ = lim f(x), lim f(x) = 0, and
→-1-
→-1+
x→2-
I→2+
x→∞
• the table of signs for
a.
f'(x)
f' and f" are given below:
-∞, -1)
-1
und.
und.
(-1,1) 1 (1,2)
+ 0 + und.
0 + und.
2 (2, +∞0)
+
Give equations of the three linear asymptotes of the graph of f.
b.
Determine the intervals where f is increasing or decreasing and where f is concave
up or concave down. Identify the relative extremum points and points of inflection, if there
are any.
Sketch the graph of f with emphasis on concavity. Label all the intercept points,
relative extremum points, and inflection points with their respective coordinates, and the
asymptotes with their respective equations.
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