Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 4 - Applications of the Derivative - 4.1 Linear Approximation and Applications - Exercises - Page 174: 46



Work Step by Step

Linearization of $ f(x)$ at $ x=a $ is $ L(x)=f(a)+f'(a)(x-a)$ Knowing that $ f(x)=\frac{1}{x}$, $ f'(x)=-\frac{1}{x^{2}}$ and $ a=2$, we have $ L(x)=\frac{1}{2}-\frac{1}{2^{2}}(x-2)=\frac{1}{2}-\frac{x}{4}+\frac{1}{2}=1-\frac{x}{4}=\frac{4-x}{4}$
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