State two advantages that Newton's method has over the bisection method. Problem 3 Use Newton's method to determine an approximation to the solution to cos(x)x=0 that lies in the interval [0,2]. Find the approximation to six decimal places (in this case, you only need to compute up to the case where n=4 ). If xn is an approximation of a solution in f(x)=0 and if the derivative (f(x)=0), then the next approximation is given by, xn+1=xnf(xn)f(xn)