$(40/100)$ Using the algorithms described in the class notes $($Lecture$-3)$ design two functions $($you may use the m$-$language and work in Matlab or use any high$-$level language$)$: one of them should utilize the secant method and another one should utilize the false position $("$regula falsi"$)$ method for solving nonlinear equations f$($x$)=0.$

These functions must use the following calling arguments:

initial approximations x$\_(1),$x$\_(2),$ delta $($pre$-$determined tolerance value$),$ a function utilizing f$($x$),$ a flag determining a stopping criterion. Your functions shall return a root, which was found, and the number of iterations needed to find it$.$

Your function shall give the user $4$ options to stop the iterative process and have $3$ corresponding branches, accordingly $($an option to be chosen must be the Flag argument in your respective function$)$:

a$)$ An absolute approximate error is used to stop the process. You may predict the number of iterations in advance in such a case.

b$)$ An absolute relative approximate error is used to stop the process.

c$)$ Estimation of a true absolute error is used to stop the process.

d$)$ Conjunction of an absolute approximate error and an estimated true absolute error is used to stop the process. You need to comment on every single line of your functions explaining what this line of your code stands for.