Sketch a graph of a rational function that satisfies the following conditions f(0) = 0, f(-4) = 2, f(4) = -2 f(x) is undefined for x = + 2, -2 f '(-4) = f '(0) = f '(4) = 0 f '(x) < 0 for x < -4, x > 4 f '(x) > 0 for -4 < x < -2, -2 < x < 0 and 0 < x < 2, 2 < 4 f ''(0) = 0 f ''(x) > 0 for x < -2, 0 < x < 2 f ''(x) < 0 for -2 < x < 0, x > 2
Sketch a graph of a rational function that satisfies the following conditions f(0) = 0, f(-4) = 2, f(4) = -2 f(x) is undefined for x = + 2, -2 f '(-4) = f '(0) = f '(4) = 0 f '(x) < 0 for x < -4, x > 4 f '(x) > 0 for -4 < x < -2, -2 < x < 0 and 0 < x < 2, 2 < 4 f ''(0) = 0 f ''(x) > 0 for x < -2, 0 < x < 2 f ''(x) < 0 for -2 < x < 0, x > 2
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 54E
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Sketch a graph of a rational function that satisfies the following conditions
f(0) = 0, f(-4) = 2, f(4) = -2
f(x) is undefined for x = + 2, -2
f '(-4) = f '(0) = f '(4) = 0
f '(x) < 0 for x < -4, x > 4
f '(x) > 0 for -4 < x < -2, -2 < x < 0 and
0 < x < 2, 2 < 4
f ''(0) = 0
f ''(x) > 0 for x < -2, 0 < x < 2
f ''(x) < 0 for -2 < x < 0, x > 2
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