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Given the function f(x) = x³+2x² (x-1)² with f'(x) = x³-3x²-4x (x-1)³ } and f'(x) = 14x+4 (x-1)4 a. Using limits, how that the lines with the equation x = 1 and y = x + 4 are asymptotes of the graph of f. b. Identify the critical number, and the possible points of inflection of the graph of f.

Given the function f(x) = x³+2x² (x-1)² with f'(x) = x³-3x²-4x (x-1)³ } and f'(x) = 14x+4 (x-1)4 a. Using limits, how that the lines with the equation x = 1 and y = x + 4 are asymptotes of the graph of f. b. Identify the critical number, 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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Given the function f(x) = x³+2x² (x-1)² with f'(x) = x³-3x²-4x (x-1)³ II. ) and f'(x) = 14x+4 (x-1)4 a. Using limits, how that the lines with the equation x = 1 and y = x + 4 are asymptotes of the graph of f. b. Identify the critical number, and the possible points of inflection of the graph of f. c. Construct a table of signs for f'andf". Specify the following: I. The intervals on which the graph f is increasing, decreasing, concave up, and concave down The values of x at which fhas relative extrema, inflection points, and vertical asymptotes (if any) d. Sketch the graph of y = f(x) with emphasis on concavity. Label all the intercept points, relative extremum points, and inflection points with their coordinates. Show the asymptotes of the graph off and label them with their respective equations.
Transcribed Image Text:Given the function f(x) = x³+2x² (x-1)² with f'(x) = x³-3x²-4x (x-1)³ II. ) and f'(x) = 14x+4 (x-1)4 a. Using limits, how that the lines with the equation x = 1 and y = x + 4 are asymptotes of the graph of f. b. Identify the critical number, and the possible points of inflection of the graph of f. c. Construct a table of signs for f'andf". Specify the following: I. The intervals on which the graph f is increasing, decreasing, concave up, and concave down The values of x at which fhas relative extrema, inflection points, and vertical asymptotes (if any) d. Sketch the graph of y = f(x) with emphasis on concavity. Label all the intercept points, relative extremum points, and inflection points with their coordinates. Show the asymptotes of the graph off and label them with their respective equations.
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