Question# $2($CH$3)$

$12.$ Construct the divided$-$difference table from these data:

$x,-0\mathrm{.}2,0\mathrm{.}3,0\mathrm{.}7,-0\mathrm{.}3,0\mathrm{.}1$

$f(x),1\mathrm{.}23,2\mathrm{.}34,-1\mathrm{.}05,6\mathrm{.}51,-0\mathrm{.}06$

Use the divided$-$difference table from Exercise $12$ to interpolate for $f(0\mathrm{.}4)$

a$.$ Using the first three points.

b$.$ Using the last three points.

c$.$ Using the best set of three points. Which points should be used?

d$.$ Using the best set of four points.

e$.$ Using all of the points.

f$.$ Explain why the results are not all the same.