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1. Given: - Ar with f'(x): (x+ 2)2 r(x + 8)(x – 2) (r +2)3 8(7x-4) (r +2)4 S(x) = and f"(x) = a. Find the domain of f and the intercepts of the graph of f. b. Using limits, show that r=-2 and y = r-8 are asymptotes of the graph of f. c. Identify the critical mumbers of f and the possible points of inflection of the graph of f.

1. Given: - Ar with f'(x): (x+ 2)2 r(x + 8)(x – 2) (r +2)3 8(7x-4) (r +2)4 S(x) = and f"(x) = a. Find the domain of f and the intercepts of the graph of f. b. Using limits, show that r=-2 and y = r-8 are asymptotes of the graph of f. c. Identify the critical mumbers of f and the possible points of inflection of the graph of f.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1. Given: 7- 4r r(r +8)(r – 2) 8(7x – 4) (r + 2)4 f(x) = (x+ 2)2 with f'(r) = and f"(r) = (r +2)3 a. Find the domain of f and the intercepts of the graph of f. b. Using limits, show that r= -2 and y = r- 8 are asymptotes of the graph of f. c. Identify the critical mumbers 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 ofr at which f 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:1. Given: 7- 4r r(r +8)(r – 2) 8(7x – 4) (r + 2)4 f(x) = (x+ 2)2 with f'(r) = and f"(r) = (r +2)3 a. Find the domain of f and the intercepts of the graph of f. b. Using limits, show that r= -2 and y = r- 8 are asymptotes of the graph of f. c. Identify the critical mumbers 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 ofr at which f 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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