Answer
$L(x)=-x-5$
Work Step by Step
Step 1. $f(x)=2x^2+3x-3$, $f'(x)=4x+3$,
Step 2. Choose $x=-1$, $f(-1)=2(-1)^2+3(-1)-3=-4$, $f'(-1)=-4+3=-1$,
Step 3. The linearization at $x=-1$ is $L(x)=f(-1)+f'(-1)(x+1)=-4-(x+1)=-x-5$
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: 9
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