Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.3 Exercises - Page 126: 79

Answer

$f’(x) = \frac{6}{(x+2)^{2}}$ $g’(x) = \frac{6}{(x+2)^{2}}$ The slope of f(x) is equal to the slope of g(x). They are parallel fucntions.
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Work Step by Step

Quotient rule: $\frac{d}{dx}$$\frac{f(x)}{g(x)}$ = $\frac{g(x)f’(x)-f(x)g’(x)}{g(x)g(x)}$ $f(x) = \frac{3x}{x+2}$ $f’(x) = \frac{(x+2)(3)-(3x)(1)}{(x+2)^{2}}$ = $\frac{3x+6-3x}{(x+2)^{2}}$ = $\frac{6}{(x+2)^{2}}$ $g(x) = \frac{5x+4}{x+2}$ $g’(x) = \frac{(x+2)(5)-(5x+4)(1)}{(x+2)^{2}}$=$\frac{5x-10-5x-4}{(x+2)^{2}}$=$\frac{6}{(x+2)^{2}}$
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