1. Consider the function f(x) = r+1+ Note that r -4 1² – 4 r*(r² – 12) f'(x) 82(r² + 12) (1* – 4)ª and f"(x) = (2² – 4)² and the z-intercept of the graph of f is approximately z a 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 z at which f has relative extrema, inflection points, and vertical asymptotes (if any). (c) Sketch the graph of ƒ 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-
1. Consider the function f(x) = r+1+ Note that r -4 1² – 4 r*(r² – 12) f'(x) 82(r² + 12) (1* – 4)ª and f"(x) = (2² – 4)² and the z-intercept of the graph of f is approximately z a 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 z at which f has relative extrema, inflection points, and vertical asymptotes (if any). (c) Sketch the graph of ƒ 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-
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 54E
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