5. For the function: x + 3 (x² - 4) f(x) = a) Find the domain. ƒ'(x) = -x² - 6x-4 (x² − 4)² f"(x) = 2(x³ + 9x² + 12x + 12) (x² − 4)³ b) Find vertical and horizontal asymptotes. Examine vertical asymptote on either side of the discontinuity.

5. For the function: x + 3 (x² - 4) f(x) = a) Find the domain. ƒ'(x) = -x² - 6x-4 (x² − 4)² f"(x) = 2(x³ + 9x² + 12x + 12) (x² − 4)³ b) Find vertical and horizontal asymptotes. Examine vertical asymptote on either side of the discontinuity.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.5: Polynomial And Rational Functions

Problem 41E

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Question

Please help with all subparts. Thanks! I BEG OF YOU,

5. For the function:
x + 3
(x² - 4)
f(x) =
-
a) Find the domain.
c) Find all intercepts.
f'(x) =
d) Find critical point(s).
-x² - 6x- 4
(x² - 4)²
f"(x) =
b) Find vertical and horizontal asymptotes. Examine vertical asymptote on either side of the
discontinuity.
2(x³ +9x² + 12x + 12)
(x² - 4)³

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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