$***$ You are required to find a root of one of the functions given below by using the methods taught in the class which include $($a$)$Bisection method, $($b$)$Newton$\text{'}$s method, $($c$)$Secant method and $($d$)$Fixed point iteration method.

& Calculate the true percent relative error $({}_t)$ in each iteration step for each method and plot it with respect to the iteration number. Plot all four relative errors in one graph and comment on the comparison of these methods.

Note that there are three different functions $($f$1,$ f$2,$ f$3)$ which are assigned to certain Student ID numbers. You must work with the function which is associated to your ID number. Do not choose functions randomly.

You can perform the calculations by modifying the Matlab codes given in lecture notes. Contain the program code you have written, plots and your comments in a single pdf file.

$f2(x)=x^2-cosh(x)$

Determine a true relative error $(($:${}_1$