Question $1$: In maximum likelihood estimation, the estimator is obtained by maximizing

the $log$ likelihood function. However, most of the log likelihood has to be optimized by

Newton$-$Raphson algorithm. In this question, we will learn to program Newton$-$Raphson

algorithm for a univariate function. Consider the function $f()=\frac{3{}^2-1}{1+{}^3},>0.$ Use the

Newton$-$Raphson method to find the maximizer of the function. Implement the algorithms

in $R$ and run your code to obtain the maximizer. $($Attach your screenshots of the output

in R$).$ You can use the online symbolic differentiation calculator to obtain $f^{\text{'}}()$ and $f^{\text{'}\text{'}}()$