Q$1.$ Use Newton's interpolating polynomial to determine y at $x=8$ to the best possible accuracy. Compute the finite divided differences as in Fig. $17\mathrm{.}5$ and order your points to attain optimal accuracy and convergence. That is$,$ the points should be centered around and as close as possible to the unknown.

$\backslash$table$[[x,0,1,2,5\mathrm{.}5,11,13,16,18],[y,0\mathrm{.}5,3\mathrm{.}134,5\mathrm{.}3,9\mathrm{.}9,10\mathrm{.}2,9\mathrm{.}35,7\mathrm{.}2,6\mathrm{.}2]]$