A function is given as$,$

f$($x$)=$ x$^3-8$x$^2+12$x$-4$

Start with initial guess x$\_0=6\mathrm{.}5,$ determine one root using

a$)$ Newton$-$Raphson Method

b$)$ Fixed point iteration

c$)$ Modified secant method with perturbation factor $0\mathrm{.}001$

d$)$ Using MATLAB and using all three methods

Provide detail hand calculations for problem a to c$.$

Provide screenshot of all three M$-$files and corresponding command window with results.