This x-intercept will typically be a better approximation to the function's root than the original guess, and the method can be iterated. The idea of the method is as follows: one starts with an initial guess which is reasonably close to the true root, then the function is approximated by its tangent line (which can be computed using the tools of calculus), and one computes the x-intercept of this tangent line (which is easily done with elementary algebra). We see that x n+1 is a better approximation than x n for the root x of the function f. The function ƒ is shown in blue and the tangent line is in red.

3.1 Difficulty in calculating derivative of a function.