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: 55



Work Step by Step

Linearization of $ f(x)$ at $ x=a $ is $ L(x)=f(a)+f'(a)(x-a)$ Therefore, the linearization at x=2 is $ L(x)=f(2)+f'(2)(x-2)$ $\implies f(2)+f'(2)(x-2)=2x+4$ $\implies f(2)+f'(2)\times x+f'(2)\times-2=2x+4$ $\implies f'(2)=2$ and $ f(2)-2\times f'(2)=4$ which gives $ f(2)=4+(2\times f'(2))=4+(2\times2)=8$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.