In MATLAB Please

Problem 3: Applications of the Newton-Raphson Method a) Use graphical methods to estimate all the roots of the function f(x) = x3 e2* sin(x) in the interval [0, 20). (Remember the graph scaling technique!) b) Use Newtonroot to find the three roots of the unscaled equation f(x) = x3 e2* sin(x). Use the values of maxtol=0.001, maxitr=20 and choose your own values x1. c) Repeat part b using the scaled version of the equation. Compare the rate of convergence (number of iterations) between using the unscaled and the scaled equations. Is it necessary to use the scaled equation in order to obtain the solution efficiently? d) Discuss the potential difficulties in applying the Newton-Raphson method. Critical thinking: The point of this problem is to understand the sufficient condition for convergence for these so-called open methods to solve f(x) = 0 with the help of the graphical method. When the slope of the iterative function g(x) is steep around a specific root, no convergence to that root would be expected. For Newton-Raphson method, when the slope of f(x) is close to zero around a specific root (hence the slope for g(x) is steep), convergence of the algorithm to that root is usually not achieved. The Newton algorithm will instead converge to another root, if applicable. In this problem, we apply the fixed-point and Newton root-finding functions to observe these phenomena. Problem 3: Applications of the Newton-Raphson Method a) Use graphical methods to estimate all the roots of the function f(x) = x3 e2* sin(x) in the interval [0, 20). (Remember the graph scaling technique!) b) Use Newtonroot to find the three roots of the unscaled equation f(x) = x3 e2* sin(x). Use the values of maxtol=0.001, maxitr=20 and choose your own values x1. c) Repeat part b using the scaled version of the equation. Compare the rate of convergence (number of iterations) between using the unscaled and the scaled equations. Is it necessary to use the scaled equation in order to obtain the solution efficiently? d) Discuss the potential difficulties in applying the Newton-Raphson method. Critical thinking: The point of this problem is to understand the sufficient condition for convergence for these so-called open methods to solve f(x) = 0 with the help of the graphical method. When the slope of the iterative function g(x) is steep around a specific root, no convergence to that root would be expected. For Newton-Raphson method, when the slope of f(x) is close to zero around a specific root (hence the slope for g(x) is steep), convergence of the algorithm to that root is usually not achieved. The Newton algorithm will instead converge to another root, if applicable. In this problem, we apply the fixed-point and Newton root-finding functions to observe these phenomena