Problem $2$:$($Program$)$

Write a program in MATLAB that implements the third derivative of the function.

$f(x)=xcos(x)$

from $x=1$ to $x=2$ with a spacing $h=0\mathrm{.}05.$

a$.$ The program must implement the four$-$point forward, four$-$point central, and four$-$point backward difference formulas for the third derivative given below. The program must be

valid for any spacing $h.$

b$.$ The program must display the results in a table of $4$ columns, with the value of $x_i,f^{\text{'}\text{'}\text{'}}(x_i)-$forward,f$"\text{'}(\{$:$x_i)-$backward, $f^{\text{'}\text{'}\text{'}}(x_i)-$central

c$.$ The program must show a plot of $f^{\text{'}\text{'}\text{'}}(x)$ vs$.x$ using the three methods. Plot also the exact derivative $f^{\text{'}\text{'}\text{'}}(x)=xsin(x)-3cos(x).$ Use circle markers $($red$,$ blue, green$)$ for the

numerical values and a solid black line for the exact derivative.