QUESTION $1$

Consider the function

$f(x)=x^3+4x^2-10$

$($a$)$ Determine a root of $f(x)$ in the interval $1,2$ to four significant figures, involving at least five iterations,

$(5)$

using the bisection method.

$(5)$

$($b$)$ Repeat the question using the $x=g(x)$ method.

$($c$)$ Reprat the question using the Newton's method.

$($d$)$ Calculate the error involved in Niewton's method:

$($e$)$ Write a program that can calculate the root using Newtor's method, and also determine the error involved.

$[25]$