Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 9 - Exponents and Exponential Functions - 9.4 Taylor Polynomials - Preliminary Questions - Page 492: 4



Work Step by Step

For a function $f(x)$ satisfying $\left|f^{(4)}(x)\right| \leq 1$ for all $x$, we have: \begin{align*} \left|T_{3}(2)-f(2)\right| &\leq \frac{1}{24}\left|f^{(4)}(x)\right| 2^{4} \\ &\leq \frac{16}{24}\lt\frac{2}{3} \end{align*} Thus, the correct answer is (b).
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