Use Newton's interpolating polynomial to determine y at x = 3.5 to the best possible accuracy. Compute the finite divided differences as in Fig. 18.5 and order your points to attain optimal accuracy and convergence.
Figure 18.5
Graphical depiction of the recursive nature of finite divided differences.

Third f(x First Second x2, x, x flxol flxil flx2 Xx1, 2.5 4.5 y 2 5.4375 7.3516 7.5625 8.4453 9.1875 12