5. For the function: x3 f(x) = f'(x) = (x+2) 2x3 + 6x2 (x + 2)² ₤"(x) 2x312x2 +24x (x+2)³ a) Find the domain. b) Find vertical and horizontal asymptotes. Examine vertical asymptote on either side of the discontinuity. c) Find all intercepts. d) Find critical point(s). e) Find any local extrema. f) Find point(s) of inflection. g) Sketch. Include labels for: intercepts, asymptotes, critical point(s), and point(s) of inflection.
5. For the function: x3 f(x) = f'(x) = (x+2) 2x3 + 6x2 (x + 2)² ₤"(x) 2x312x2 +24x (x+2)³ a) Find the domain. b) Find vertical and horizontal asymptotes. Examine vertical asymptote on either side of the discontinuity. c) Find all intercepts. d) Find critical point(s). e) Find any local extrema. f) Find point(s) of inflection. g) Sketch. Include labels for: intercepts, asymptotes, critical point(s), and point(s) of inflection.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 15T
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Transcribed Image Text:5. For the function:
x3
f(x) =
f'(x) =
(x+2)
2x3 + 6x2
(x + 2)²
₤"(x)
2x312x2 +24x
(x+2)³
a) Find the domain.
b) Find vertical and horizontal asymptotes. Examine vertical asymptote on either side of the
discontinuity.
c) Find all intercepts.
d) Find critical point(s).
e) Find any local extrema.
Transcribed Image Text:f)
Find point(s) of inflection.
g) Sketch. Include labels for: intercepts, asymptotes, critical point(s), and point(s) of inflection.
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