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f(x)= f"(x) = x³ x²-4 8x(x² +12) (x²-4)³ with f'(x) = x²(x² - 12) (x² - 4)² and (a) Find the intercepts of the graph of f. (b) Verify that the lines x = 2, x = -2, and y = x are the asymptotes of the graph of f. (c) Identify the critical numbers and possible points of inflection.

f(x)= f"(x) = x³ x²-4 8x(x² +12) (x²-4)³ with f'(x) = x²(x² - 12) (x² - 4)² and (a) Find the intercepts of the graph of f. (b) Verify that the lines x = 2, x = -2, and y = x are the asymptotes of the graph of f. (c) Identify the critical numbers and possible points of inflection.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 7E
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f(x) = x-3 x²-4' with f'(x)= 8x(x²+12) (x²-4)³ x²(x² - 12) (x² - 4)² and f"(x) = (a) Find the intercepts of the graph of f. (b) Verify that the lines x = 2, x = -2, and y = x are the asymptotes of the graph of f. (c) Identify the critical numbers and possible points of inflection. (d) Make a table showing the intervals where f is increasing or decreasing, where the graph of f is concave up or concave down. Specify all relative minimum points, relative maxi- mum points, and points of inflection of the graph of f. (e) Sketch the graph of f. Label the intercepts, relative extremum points, and points of inflection with their coordinates. Draw the asymptotes and label them with their equations.
Transcribed Image Text:f(x) = x-3 x²-4' with f'(x)= 8x(x²+12) (x²-4)³ x²(x² - 12) (x² - 4)² and f"(x) = (a) Find the intercepts of the graph of f. (b) Verify that the lines x = 2, x = -2, and y = x are the asymptotes of the graph of f. (c) Identify the critical numbers and possible points of inflection. (d) Make a table showing the intervals where f is increasing or decreasing, where the graph of f is concave up or concave down. Specify all relative minimum points, relative maxi- mum points, and points of inflection of the graph of f. (e) Sketch the graph of f. Label the intercepts, relative extremum points, and points of inflection with their coordinates. Draw the asymptotes and label them with their equations.
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