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a3 – 4x2 (x + 2)² ' x(x +8)(x – 2) (x + 2)³ 8(7x - 4) f(x) with f'(x) = and f"(x) : %3D (x + 2)ª * 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 asymptotes of the graph of f. c. Identify the critical numbers of f and the possible points of inflection of the graph of f.

a3 – 4x2 (x + 2)² ' x(x +8)(x – 2) (x + 2)³ 8(7x - 4) f(x) with f'(x) = and f"(x) : %3D (x + 2)ª * 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 asymptotes of the graph of f. c. Identify the critical numbers of f and the possible points of inflection of the graph of f.

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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x3 – 4.x2 x(x+8)(x – 2) (x + 2)³ 8(7x – 4) (x + 2)ª ´ f(x) (x + 2)² ’ with f'(x) = and f"(x) = %3D %3D %3D 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 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". From here, specify 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 ƒ has relative extrema, inflection points, and vertical asymp- totes (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 asymptotes of the graph of f and label them with their respective equations.
Transcribed Image Text:x3 – 4.x2 x(x+8)(x – 2) (x + 2)³ 8(7x – 4) (x + 2)ª ´ f(x) (x + 2)² ’ with f'(x) = and f"(x) = %3D %3D %3D 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 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". From here, specify 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 ƒ has relative extrema, inflection points, and vertical asymp- totes (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 asymptotes of the graph of f and label them with their respective equations.
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