x²(x² – 12)(x² – 4)²8x(x² + 12)(x² – 4)³ °Given: f(x)with f'(x) =and f"(x)x² – 4'(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 thegraph of f is concave up or concave down. Specify all relative minimum points, relativemaximum points, and points of inflection of the graph of f.(e) Sketch the graph of f. Label the intercepts, relative extremum points, and points ofinflection with their coordinates. Draw the asymptotes and label them with theirequations.

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Answered: Given: f(x) x2 with f'(x) = 4' x²(x² –…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.10: Partial Fractions

Problem 2E

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Given: f(x) x2 with f'(x) = 4' x²(x² – 12) (x² – 4)² 8x(x² + 12) (x² – 4)3 ° 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.