-2x-2 4x+ 8 Given f(x) f" (x) = (x – 1)2 ' (æ – 1)2 ' J'(æ) = (x - 1)3 (x - 1)4 a. Find the domain, intercepts and asymptotes of f, if any. b. Find the critical numbers of f. c. Find the values of x for the possible points of inflection.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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2x
-2x-2
4x + 8
Given f(x)
f' (x):
, f" (x) =
%3D
%3D
(x - 1)² *
(x - 1)3
(x- 1)4
a. Find the domain, intercepts and asymptotes of f, if any.
b. Find the critical numbers of f.
c. Find the values of a for the possible points of inflection.
d. Construct the sign chart or table of values.
Based on your sign chart or table of values,
e. Identify the intervals where f is increasing or decreasing.
F. Find the intervals where the graph of fis concave upward or downward.
G. Find the local maximum and minimum values of fand its inflection points, if any.
H. Sketch the graph of f. Label all important points
Transcribed Image Text:2x -2x-2 4x + 8 Given f(x) f' (x): , f" (x) = %3D %3D (x - 1)² * (x - 1)3 (x- 1)4 a. Find the domain, intercepts and asymptotes of f, if any. b. Find the critical numbers of f. c. Find the values of a for the possible points of inflection. d. Construct the sign chart or table of values. Based on your sign chart or table of values, e. Identify the intervals where f is increasing or decreasing. F. Find the intervals where the graph of fis concave upward or downward. G. Find the local maximum and minimum values of fand its inflection points, if any. H. Sketch the graph of f. Label all important points
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