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-12(3x² + 4) (x² – 4)3 -2(12 – 1) f (x) = 12x and f"(x) = 1. Let f (x) = %3D x2 - 4 (x² – 4)² ' (a) State the domain of the f. (b) Type of symmetry. (Even, Odd or Neither) (c) Find all x-intercept(s) (or state they don't exist).

-12(3x² + 4) (x² – 4)3 -2(12 – 1) f (x) = 12x and f"(x) = 1. Let f (x) = %3D x2 - 4 (x² – 4)² ' (a) State the domain of the f. (b) Type of symmetry. (Even, Odd or Neither) (c) Find all x-intercept(s) (or state they don't exist).

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 8E
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-12(3r2 + 4) (x2 – 4)3 -2(x² – 1) 12x 1. Let f(x)= f'(x) = and f"(x) = x² – 4 (x² – 4)² ' - - (a) State the domain of the f. (b) Type of symmetry. (Even, Odd or Neither) (c) Find all x-intercept(s) (or state they don't exist). (d) Find all y-intercept(s) (or state they don't exist). (e) Find the vertical and horizontal asymptotes of the function f(x) (show all work). (f) Find the critical points of f(x). Find the open interval(s) where f(x) is increasing and the open interval(s) where f(x) is decreasing (show all work). (g) State the coordinates of any local maxima and local minima. (h) Find the open interval (s) where f(x) is concave up, and where f(x) is concave down. Find any inflection points (show all work). (i) Sketch the curve, and label on your curve all the information found in part (a) - (e).
Transcribed Image Text:-12(3r2 + 4) (x2 – 4)3 -2(x² – 1) 12x 1. Let f(x)= f'(x) = and f"(x) = x² – 4 (x² – 4)² ' - - (a) State the domain of the f. (b) Type of symmetry. (Even, Odd or Neither) (c) Find all x-intercept(s) (or state they don't exist). (d) Find all y-intercept(s) (or state they don't exist). (e) Find the vertical and horizontal asymptotes of the function f(x) (show all work). (f) Find the critical points of f(x). Find the open interval(s) where f(x) is increasing and the open interval(s) where f(x) is decreasing (show all work). (g) State the coordinates of any local maxima and local minima. (h) Find the open interval (s) where f(x) is concave up, and where f(x) is concave down. Find any inflection points (show all work). (i) Sketch the curve, and label on your curve all the information found in part (a) - (e).
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