Write a Matlab function called Root_NR that finds the root of a function using the Newton-Raphson Method. (25 points) - The input parameters are the name of the function and its derivative as well as the initial estimate for the root x0 - The output is the value of the root x - The function prints out intermediate root approximations and error estimates Note: Attach Matlab function Root_NR in your .pdf lab report: Sub-question (2) - Algorithm Testing Test your function Root_NR with the simple function given below. Find both roots of this function and comment on the results. In particular, comment on the effect of the different choices of the initial guess. (15 points) f(x)=x2511x+2528 NOTE: - You can use plotfunc created previously in Lab 2 to plot f(x)=x2511x+2528 within the range [4,4]. Submitting the plot in the PDF file is optional (not to be marked). But the plot helps you understand the question better. - Round your final answers to 3 decimal places, e.g. 1.235 for 1.23456 - For the convergence criterion, use the Relative Approximate Error with the tolerance 105 - The initial estimate of the root in the table given below is 2.1 Maximum iteration: NOTE: - In order to find both roots, use different values for the initial guess in your function Root_NR - Root 1 is less than Root 2 Root 1: Root 2: Note: Provide the code outputs and the comments on the results in your lab report: Sub-question (3) - Algorithm Improvement Test your function Root_NR with the simple function given below. Find both roots of this function, answer the following questions and comment on the results. In particular, comment on the error estimates and measure of convergence as well as the effect of the different choices of the initial guess. (15 points) f(x)=x2+23x NOTE: - You can use plotfunc created previously in Lab 2 to plot the function f(x)=x2+23x within the range [4,4]. Submitting the plot in the PDF file is optional (not to be marked). - Round your final answers to 3 decimal places, e.g. 1.235 for 1.23456 - For the convergence criterion, use the Absolute Approximate Error with the tolerance 1010 - The initial estimate of the root in the table given below is 0.7 NOTE: - In order to find both roots, use different values for the initial guess in your function Root_NR - Root 1 is less than Root 2 Root 1: Root 2