(e) Sketch the graph of ƒ with emphasis on concavity. Label all the intercept points, relative extremum points, and inflection points with their coordinates. Show the linear asymptotes of the graph of f and label them with their respective equations.
(e) Sketch the graph of ƒ with emphasis on concavity. Label all the intercept points, relative extremum points, and inflection points with their coordinates. Show the linear asymptotes of the graph of f and label them 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
Related questions
Question
Please answer (e). Thank you
Transcribed Image Text:r* – 4x2
r(x + 8)(x – 2)
8(7x – 4)
Given: f(x) =
with f'(x) =
and f"(x) =
(x+ 2)?
(r+ 2)³
3
(r+ 2)4
(a) Find the domain of f and the intercepts of the graph of f.
(b) Using limits, show that r = -2 and y = x – 8 are linear asymptotes of the graph of f.
(c) Identify the critical numbers of f and the possible points of inflection of the graph of f.
(d) Construct a table of signs for f' and f". Specify the following:
i. the intervals on which f is increasing or decreasing, and on which the graph of ƒ is concave
up or concave down, and
ii. the values of r at which f has relative extrema, inflection points, and vertical asymptotes
(if any).
(e) Sketch the graph of f with emphasis on concavity. Label all the intercept points, relative
extremum points, and inflection points with their coordinates. Show the linear asymptotes of
the graph of f and label them with their respective equations.
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