% This function creates and returns a handle to the linear function
% through ( x1, f(x1) ) and ( x1+h, f(x1+h) )... in other words the
% function for the secant to f through those two points.

% f    handle to a function
% x1   start of interval
% h    length of interval (should be non-zero)
function  sec = secantLine( f, x1, h )

if (sum(h==0)) 
	error('secantLine:', "Can\'t compute a secant over an empty interval.");
end

slope = ( f(x1+h) - f(x1) ) ./ h;
% Build a string representation of anonymous function for the secant line.
str = [ '@(x)' num2str( f(x1) ) '+' num2str( slope ) '.* (x -' num2str(x1) ')' ];

% Evaluate and return the string.
sec = eval( str );