(Numerical analysis) Here's a challenging problem for those who know a little calculus. The Newton-Raphson method can be used to find the roots of any equation y(x) = 0. In this method, the (i + 1)st approximation, Xi+1, to a root of y(x) = 0 is given in terms of the ith approximation, xi, by the following formula, where y denotes the derivative of y(x) with respect to x: For example, if y) = 3x2 + 2x - 2, then y'(x) = 6x + 2, and the roots are found by making a reasonable guess for a first approximation xy and iterating by using this equation: *;+1 = x;-(3x2 + 2x - 2)/(6x + 2) a. Using the Newton-Raphson method, find the two roots of the equation 3x2 + 2x - 2 = 0. (Hint: There's one positive root and one negative root.) b. Extend the program written for Exercise 6a so that it finds the roots of any function y(x) = 0, when the function for y(x) and the derivative of y(x) are placed in the code. (Numerical analysis) Here's a challenging problem for those who know a little calculus. The Newton-Raphson method can be used to find the roots of any equation y(x) = 0. In this method, the (i + 1)st approximation, Xi+1, to a root of y(x) = 0 is given in terms of the ith approximation, xi, by the following formula, where y denotes the derivative of y(x) with respect to x: For example, if y) = 3x2 + 2x - 2, then y'(x) = 6x + 2, and the roots are found by making a reasonable guess for a first approximation xy and iterating by using this equation: *;+1 = x;-(3x2 + 2x - 2)/(6x + 2) a. Using the Newton-Raphson method, find the two roots of the equation 3x2 + 2x - 2 = 0. (Hint: There's one positive root and one negative root.) b. Extend the program written for Exercise 6a so that it finds the roots of any function y(x) = 0, when the function for y(x) and the derivative of y(x) are placed in the code