Exercise on Cubic Spline:

The following data were obtained from a function

$($a$)$ Using cubic spline and Boundary Condition $1,$ set up the matrix equation and solve for the second derivatives $($M$\text{'}$s$)$ at the nodes.

$($b$)$ Using the appropriate cubic spline equation, determine the value of the function when $x=0\mathrm{.}25.$

$\backslash$table$[[x,0,0\mathrm{.}5,1\mathrm{.}0,1\mathrm{.}5,2\mathrm{.}0],[f(x),1,1\mathrm{.}6487,2\mathrm{.}7183,4\mathrm{.}4817,7\mathrm{.}3891]]$