Question: Use Newton's interpolating polynomial to determine y at x = 8 to the best possible accuracy. Compute the finite divided differences as in Fig. 18.5

Use Newton's interpolating polynomial to determine y at x = 8 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 First f(x flxol fix2) Second f(x3, x2, XI, XO] Xx1, x2, x1] X0 X3 flxal x L0 25.5 11 13 1618 y0.5 3.134 5.3 9.9 10.2 9.35 7.2 6.2

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