DUE THIS IN MATLAB, AND ONLY MATLAB.

DUE THIS IN MATLAB, AND ONLY MATLAB.

1. (50 points) Math problem: Consider the function: f(x)=1+50exsinsin(3x). a. (5 points) Plot this function from x=0 to x=10 using at least 100 points. b. (5 points) Based on the plot, determine how many roots the function has in the plotted range. c. (15 points) Using any method, determine all roots in the plotted range. d. (15 points) Using five iterations of Newton's method and an initial guess of x=0.5, estimate x. Place your answers in the table below: e. (10 points) Different roots can be found using Newton's Method by changing the initial guess. However, some guesses will not work at all. What is an initial guess which will not work for this example? Hint: look at a plot of f(x) versus x