## Calculus (3rd Edition)

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).