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3 + a2 – 4 4.x = r+1+ Consider the function f(x) Note that x2 - 4 x2 - 4 a*(x² – 12) (x2 – 4)? 8.x(x2 + 12) (x2 – 4)3 - f'(x) = and f"(x) = %3D - and the x-intercept of the graph of f is approximately a 1.3146.

3 + a2 – 4 4.x = r+1+ Consider the function f(x) Note that x2 - 4 x2 - 4 a*(x² – 12) (x2 – 4)? 8.x(x2 + 12) (x2 – 4)3 - f'(x) = and f"(x) = %3D - and the x-intercept of the graph of f is approximately a 1.3146.

Advanced Engineering Mathematics
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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1. Consider the function /(r) r3 + x? – 4 4.x = r +1+ Note that 4 x2 - 4 | x(x² – 12) (x2 – 4)2 8.x(x2 + 12) (x2 – 4)3 - f'(x) = and f"(x) = and the r-intercept of the graph of f is approximately r 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 x 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.
Transcribed Image Text:1. Consider the function /(r) r3 + x? – 4 4.x = r +1+ Note that 4 x2 - 4 | x(x² – 12) (x2 – 4)2 8.x(x2 + 12) (x2 – 4)3 - f'(x) = and f"(x) = and the r-intercept of the graph of f is approximately r 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 x 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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