Recitation Problems -
1. Determine the highest real root of f(x) = 2x^{3} - 11.7x^{2} + 17.7x - 5
using the Newton-Raphson method with at least four iterations. Start with an initial guess of x_{0} = 3.
2. Determine the real roots of f(x) = -1 + 5.5x - 4x^{2} + 0.5x^{3}
Create a MATLAB script that uses the Newton-Raphson method, iterating until the relative approximate error is less than 0.01%. Also plot the function and verify the roots graphically.