Answer
$L(x)=-x+2$
Work Step by Step
Step 1. $f(x)=x^{-1}$, $f'(x)=-x^{-2}$,
Step 2. Choose $x=1$, $f(1)=1$, $f'(1)=-1$,
Step 3. The linearization at $x=1$ is $L(x)=f(1)+f'(1)(x-1)=1-(x-1)=-x+2$
Thomas' Calculus 13th Edition
by Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0-32187-896-5
ISBN 13:
978-0-32187-896-0
Chapter 3: Derivatives - Section 3.9 - Linearization and Differentials - Exercises 3.9 - Page 174: 8
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