Answer
2.16
Work Step by Step
Given/Known: $ f(x)=x^{4}$, $ a=3$, $\Delta x=0.02$ and $ f'(x)=4x^{3}$
Recall: $ f(a+\Delta x)-f(a)\approx f'(a)\Delta x $
$\implies f(3+0.02)-f(3)\approx f'(3)\Delta x=4(3)^{3}\times0.02=2.16$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
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 172: 2
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