(a) Develop an M-file function to implement Brent's root-location method. Base your fu...

(a) Develop an M-file function to implement Brent's root-location method. Base your function on Fig. 6.10, but with the beginning of the function changed to

function [b,fb] = fzeronew(f,xl,xu,varargin)% fzeronew: Brent root location zeroes% [b,fb] = fzeronew(f,xl,xu,p1,p2,...):%   uses Brent's method to find the root of f% input:%   f = name of function%   xl, xu = lower and upper guesses%   p1,p2,... = additional parameters used by f% output:%   b = real root%   fb = function value at root

Make the appropriate modifications so that the function performs as outlined in the documentation statements. In addi­tion, include error traps to ensure that the function's three required arguments (f, xl, xu) are prescribed, and that the initial guesses bracket a root.

(b) Test your function by using it to solve for the root of the function from Example 5.6 using

>> [x, fx] = fzeronew(@(x, n) x^n-1,0,1.3,10)