Use Newton divided differences' interpolating method to calculate $f(4).$

$[$:$f_f(x)=f(x)+(x-x_0)f{x}_1,x_0\}$

$+$cdots$+(i-x_0)(x-x_1)cdots(x-x_{n-1})f(x_2{x}_2-dotscdots{x}_0]$

$\backslash$table$[[x,3,5,2,6,1]]$

$\backslash$table$[[f(x_0),5\mathrm{.}25],[f[x_1,x_0],7\mathrm{.}25],[f[x_2,x_1],5\mathrm{.}25],[f[x_3,x_2],8],[f[x_4,x_3],6\mathrm{.}25]]$