Please answer (b). Thank you r* – 4x2r(x + 8)(x – 2)8(7x – 4)Given: f(x) =with f'(x) =and f"(x) =(x+ 2)?(r+ 2)³3(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 concaveup or concave down, andii. 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, relativeextremum points, and inflection points with their coordinates. Show the linear asymptotes ofthe graph of f and label them with their respective equations.

(b) Given that, the function is fx=x3-4x2x+22. limx→-2fx=limx→-2x3-4x2x+22=-23-4-22-2+22=-240=-∞…

Answered: (b) Using limits, show that r = -2 and…

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(b) Using limits, show that r = -2 and y = r – 8 are linear asymptotes of the graph of f.

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

ChapterP: Prerequisites

SectionP.4: Factoring Polynomials

Problem 84E: The rate of change of an autocatalytic chemical reaction is kQxkx2 where Q is the amount of the...

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Question

Please answer (b). Thank you

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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