Sub-question (1) - Algorithm Implementation 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 The volume V of liquid in a spherical tank of radius r is related to the depth h of the liquid in the tank, as shown in Figure 1. The volume can be calculated with the formula: V=3h2(3rh) Figure 1: Spherical tank Use your function Root_NR to calculate the depth h of liquid in a spherical tank of radius r=1.2m to provide a volume of liquid V=4mm3. (15 points) NOTE: - You can use plotfunc created previously in Lab 2 to plot the function within range [2,4]. Note that we need to find the physically meaningful root here. Submitting the plot in the PDF file is optional (not to be marked). - The initial estimate of the root in the table given below is 0.048 - 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 Maximum iteration: NOTE: - The initial estimate of the root in the table given below is 0.54 - 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 Maximum iteration: h= NOTE: - The initial estimate of the root in the table given below is 2.34 - 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 Maximum iteration: h= Which one of the initial estimates converges to the physically meaningful root? Note: Attach the Matlab code outputs in your .pdf lab report