Answer
(b)
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).
