Repeat Question 13.5 using the central-difference methods of orders 2 and 4. Comment on your answers.

Question 13.5

Implement the elementary definition of a derivative to determine a converged estimate of f′(−1) for f(x) = sin(x³).

Table 13.20 Samples of an unknown function f(x) at various node points {Xn} Xn f(xn) - 2 -1.9 -1.8 -1.7 -1.6 -1.5 -1.4 -1.3 -1.2 -1.1 -1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 -0.6646 -0.1671 0.2639 0.6276 0.9252 1.1592 1.3331 1.4521 1.5218 1.5489 1.5403 1.5035 1.4459 1.3748 1.2971 1.2194 1.1474 1.0860 1.0392 1.0100