function [root,ea,iter]=secantmethod(func,xr,xo,es,maxit,varargin)
% Secant method that uses numerical derivative to find the solution
% 
% input:
% func = name of function
% xr = initial guess
% xo = the second x value from which to calculate the numerical derivative
% es = desired relative error (default = 0.0001%)
% maxit = maximum allowable iterations (default = 50)
% p1,p2,... = additional parameters used by function
% output:
% root = real root
% ea = approximate relative error (%)
% iter = number of iterations
if nargin<3,error('at least 3 input arguments required'),end
if nargin<4|isempty(es),es=0.0001;end
if nargin<5|isempty(maxit),maxit=50;end
iter = 0;
% Define x step size between your two points
xstep = xr-xo;
while (1)
    xrold = xr;
    %xr = xr - func(xr)/dfunc(xr); Newton Raphson method
    xr = xr - func(xr)*(xo-xr)/(func(xo)-func(xr));
    iter = iter + 1;
    if xr ~= 0, ea = abs((xr - xrold)/xr) * 100; end
    if ea <= es | iter >= maxit, break, end
    % Define new second x value for slope
    xo = xr-xstep;
end
root = xr;
end