Answer is: option3
\( 0.213 \)Solution:
The Lagrange error is
\[ |R_n(x)|=\frac{M}{(n+1)!}|x-a|^{n+1} \]
Recall that \( M \) is the upper bound for all values of the \( (n+1) \) derivative on the given interval \( [a,x] \).
When \( n=2,\; a=1,\; x=1.4,\; M=10 \), we have
\[ |R_2(1.4)| = \frac{10}{3!}|1.4-1|^3 = \frac{10}{6}(0.4)^3 \approx 0.107 \]
