Using MatLab$)$ Find a polynomial to interpolate the data after that find $f(3\mathrm{.}5).$

$f(x)$

$=b_0+b_1(x-x_0)+b_2(x-x_0)(x-x_1)+b_3(x-x_0)(x-x_1)(x-x_2)$

$+b_4(x-x_0)(x-x_1)(x-x_2)(x-x_3)$

and simular to the given code:

function coeffs$=$ newtons$\_$divided$\_$difference$($x$,$y$)$

$\%$input:

$\%$x: vector of x value

$\%$ y: vector of y value corresponding to x

$\%$ number of data of points

n$=$length$($x$)$

$\%$initialize the divided differnces table

F$=$ zeros$($n$,$n$)$

$\%$ fill in the first column with y values

F$($:$,1)=$y;

$\%$ compute the divided differences

for j$=2$:n;

for i$=1$:n$-$j$+1$;

F$($i$,$j$)=($F$($i$+1,$ j$-1)-$F$($i$,$j$-1))/($x$($i$+$j$-1)-$x$($i$))$;

end

end

$\%$ coefficients of the polynoimal

coeffs$=$ F$(1,$:$)$;

end