The following data table is sampled from the polynomialf$=2$x$^(3)+3$x$+1$

i $(01234)$

x $(0\mathrm{.}10\mathrm{.}20\mathrm{.}30\mathrm{.}40\mathrm{.}5)$

f$($x$)(1\mathrm{.}3021\mathrm{.}6161\mathrm{.}9542\mathrm{.}3282\mathrm{.}750)$

a$)$ By Handwriting, Derive a third order polynomial passing through the data

b$)$ Lagrange method f$(0\mathrm{.}25)=?$

c$)$ fit cubic spline to the above data set

d$)$ plot equations by Matlab and print it