Can't get a proper solution with modified secant method

Hi all, I have built a code for modified secant method to find the root of the function f(x)= which is given below. The output of the code should give an answer of about 0.5671 but instead it is giving 56.71.... something answer. HOw to solve this problem? Code is mentioned below:

clear all
close all
clc
n=100;
f=@(x) exp(-x)-x;
dx=0.01;
x0=1;
x(1)=x0;
i=0;
err=0.0048;
for i=1:n
    x(i+1)=x(i)-((f(x(i)*dx)/(f(x(i)+dx)-f(x(i)))));
    if abs((x(i+1)-x(i))/x(i+1))*100<err
        roots=x(i);
        break;
    end
end

disp(roots)

Answer 1

[Walter Roberson]

    x(i+1)=x(i)-((f(x(i)*dx)/(f(x(i)+dx)-f(x(i)))));

Notice that you have f(x(i)*dx) and dx is 0.01 . When you find the root of f(x(i)/100) == 0, then x(i) would be 100 times the root of f(x)

Meanwhile in the denominator you have f(x(i)+dx) with +dx not *dx . It seems to me you need to be consistent

Answer 2

[Peter]

clear all

close all

clc

n=100;

f=@(x) exp(-x)-x;

dx=0.01;

x0=1;

x(1)=x0;

i=0;

err=0.0048;

for i=1:n

x(i+1)=x(i)-((f(x(i)*dx)/(f(x(i)+dx)-f(x(i)))));

if abs((x(i+1)-x(i))/x(i+1))*100<err

roots=x(i);

break;

end

end

disp(roots)