function [root,ea,iter]=modsecantmethod(func,xr,del,es,maxit,varargin)
% Modified secant method - uses a numerical derivative to find the solution
% input:
% func = name of function
% xr = initial guess
% del = perturbation from initial guess, to calculate slope
% 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;
while (1)
    xrold = xr;
    xr = xr - del*xr*func(xr)/(func(xr+del*xr)-func(xr));
    iter = iter + 1;
    if xr ~= 0, ea = abs((xr - xrold)/xr) * 100; end
    if ea <= es | iter >= maxit, break, end
end
root = xr;
end