function [x, y, err, iter]  = secant(f,x0,x1,xtol,ytol,maxit)
% this is the secant method function
 
a = x0;
b = x1;
counter = 0;
 
while ((abs(a-b) > xtol) || (abs(feval(f,b)) > ytol)) && (counter < maxit)
    counter = counter + 1;
    xn = b - feval(f,b)*(b-a)./(feval(f,b)-feval(f,a));
    a = b;
    b = xn;
    x(counter) = b;
    y(counter) = feval(f,b);
end
iter = counter;
err = abs(b-a);




function Swrapper(f,a,b)
% this function takes a function 'f'
% and two vectors of the same size
% which correspond to the initial 
% choices in the secant method algorithm

LEN = length(a);

for i = 1:LEN
    [x, y, err, iter]  = secant(f,a(i),b(i),10^(-14),10^(-12),50);
    X(i) = x(end);
end
 
X