Python Coding:

Write a Python script that includes the following three functions:

bisection$\_$method$($f$,$ xl$,$ xr$,$ tol, max$\_$iter$)$: Implements the

Bisection method for finding the root of a function $f(x).$ The interval $,$

$xr]$ should be provided as input, along with a tolerance to $l$ and a maximum

number of iterations max$\_$iter.

false$\_$position$\_$method$($f$,$ xl$,$ xr$,$ tol, max$\_$iter$)$:

Implements the False Position $($Regula Falsi$)$ method for finding the root of a

function $f(x),$ similar to the Bisection method.

newton$\_$raphson$\_$method$($f$,$ df$,$ x$0,$ tol, max$\_$iter$)$:

Implements the Newton$-$Raphson method for finding the root of a function

$f(x),$ using its derivative $df(x).$ The starting point $x0,$ tolerance to $l,$ and

maximum number of iterations max$\_$iter should be provided as input.

Test these functions on a simple example function, such as $f(x)=x3-6x2+11x-6,$ which

has known roots at $x=1,2,3.$

Testing and Comparison:

For each method, run your function with:

Initial guesses and intervals: choose appropriate values for $xl,xr,$ and $x0$ to test

the methods.

A tolerance level of $1e-6$ and a maximum iteration count of $100.$

Record the results of the first $5$ iterations for each method, including the value of the

root approximation and the corresponding function value $f(x)$ at each step.