(8 points) This problem is focused on optimization using open methods with convergence criteria based on relative error. For this problem you are required to build separate MATLAB functions for the secant method and Newtons method to approximate a root r satisfying f (r)=0 for a given function f . We will be applying these root finding algorithms to the derivative of the functions we seek to optimize. Build your open method root finding algorithms to have the structure [xr,fr]= secant(f,x0,x1,p,nmax)[xr,fr]= newton(f,x0,p,nmax) where both methods are iterated until either the sequence of approximations has converged to p significant digits OR the number of iterations has exceeded nmax. For the purposes of this problem, let G denote a googol, that is a 1 followed by 100 zeroes: G =10100. Next consider the function3 f (x)=10G 1 x x22+ G2eG2x+G1. Using tools from first-year calculus and both of your open root finding algorithms, locate and classify all local extreme points of f . That is, apply both the secant method and Newtons method to approximate the location (i.e. x-coordinate) of all local extreme points of f to 8 significant digits. Note this may require that you choose initial guesses close enough to any local extreme points and an adequately large maximum number of iterations - there may be some trial and error involved! Then, use tools from calculus (e.g. first or second derivative test) to classify the extreme points as local max, local min, or neither.