The document provides instructions for writing a Matlab function to find roots of a function using the bisection method. It explains that the function should take the name of the function, lower and upper bounds of the interval, and a tolerance as inputs. It then provides a sample bisection function code with comments explaining that it evaluates the function at the endpoints, bisects the interval if signs are opposite, and continues bisecting until the interval is smaller than twice the tolerance or a root is found exactly. The function returns the root value.

1. Hi, Can you answer this question. Please show all your work and show important comment
sections ( Please comment what the codes of lines do!!). Please avoid command fucntions like
nargin function command. Code w/ MATLab 2015a or higher. I know hw to do the math but
failed toomany times at coding. THank you again!!! =)
Write a function file for the bisection method to find the roots of a function. Test your code on e
a functionrition. Determine what cos(x) = x 5. the following function. Determine what your
inputs and outputs should be.
Solution
The given Matlab code uses the string facility to pass the name of a function to bisection. A %
indicates the comments
function d = bisection(fn,a1,b1,tol)
% d = bisection('fn',a1,b1,tol)
%
% Â Â This function locates a root of the function fn on the interval
%Â Â [a1,b1] to within a tolerance of tol.
% Evaluating the function to the endpoints and checking if it
% changes sign.
Fa1 = feval(fn,a1);
Fb2 = feval(fn,b1);
if Fa1*Fb2 >= 0
error('Tis fn have opposite signs at a and b')

2. end
% done is used to flag the unlikely event that we find
% the root exactly before the interval has been sufficiently reduced.
done = 0;
% Bisect the interval
d = (a1+b1)/2;
% Main loop
while abs(a1-b1) > 2*tol & ~done
% Evaluate the function at the midpoint
Fc1 = feval(fn,d);
if Fa1*Fc1 < 0Â Â Â Â Â Â % The root is left of d
b1 = d;
Fb1 = Fc1;
d = (a1+b1)/2;
elseif Fc1*Fb1 < 0Â Â % The root is right of d
a1 = d;
Fa1 = Fc1;
d = (a1+b1)/2;
else              % the root
done = 1;
end
end
the file is named as bisect.m, it can be run as follows: