Solve x^3-5x^2+3x-1=0 using the bisection method in MATLAB, specifically solving with while loop. The initial limits should be -1 and 6.The while loop should stop when the absolute value of solution, f(x), is 0.001 or smaller. The code should report the number of iteration and the value of x. Please show steps and provide explanation.

My work is as follows, and, while it works, I need the code from "for" to be solved using "while"

clear; clc;

f=@(x) x^3-5*x^2+3*x-1;

xu=6; xl=-1;

if f(xl)*f(xu)>0 disp('xl and xu have not been chosen properly') end

if f(xu)<0 xs=xu; xu=xl; xl=xs; end x while> .001 || x < -.001 x_old = x; x = x - (x^3 - 5*x^2 + 3*x -1)/(3*x^2 - 10*x +3); x = (x^3 - 5*x^2 + 3*x -1); iter = iter + 1; end for n=-1:6 xm=(xu+xl)/2; if f(xm)==0 disp('This is the answer') disp(xm) disp(n) break else if f(xm)>0 xu=xm; else xl=xm; end end end

disp('answer after 5 try') disp(xm)