Given the function:

$f(x)=x^3-2x-5$

$($a$)$ Using Python as your coding language, write a program that uses the bisection

method to find the root of the function, for the interval $0,3.$ Stop the iteration

when the error as estimated by $|x_{n+1}-x_n|$ is less than ${10}^{-6}.$ Plot the output to

show the results.

$($b$)$ Repeat $($a$)$ but use the Newton$-$Raphson method to find the root of the function,

taking $x_0=2$ and using the interval as given in part $($a$).$ Plot the output to show

the results.

$(30$ marks$)$

$($c$)$ Repeat $($a$)$ but use the secant method taking $x_0=0$ and $x_1=3$ using the interval

as given. Plot the output to show the results.

$(20$ marks$)$

$($d$)$ Discuss each of the methods used for root finding and evaluate your result using

all three methods of the given function.