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: 45



Work Step by Step

Linearization of $ f(x)$ at $ x=a $ is $ L(x)=f(a)+f'(a)(x-a)$ Knowing that $ f(x)=x^{4}$, $ f'(x)=4x^{3}$ and $ a=1$, we have $ L(x)=1^{4}+4(1)^{3}(x-1)=1+4x-4=4x-3$
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