a$)$ Consider the following objective function

$mi{n}_{x}f(x)=\{x-1{)}^2(x-2)(x-3)$

$0x4$

i$)$ Use the method of Newton$-$Raphson to compute $x^{**}$ that minimizes $f(x)$ for the following three initial values of $x_0=0\mathrm{.}2,0\mathrm{.}5$ and $2\mathrm{.}5$ with ${10}^{-10}$ tolerance. $($Write MATLAB m$-$file code$)$

ii$)$ Plot the change of the $x$ versus iteration number, the alternation of the objective function by the evolution of $x$ and gradient information versus iteration number. $($Write MATLAB m$-$file code$)$