The figure below illustrates Newton's theorem for F(x) = a*x^{n} - b*e^{x} (see NewtonIterative.html ). The expression for x - F(x)/F'(x) is the one contained in the formula-object: G(x) = (n-1)*a*x^{n} + b*exp(x)*(1-x))/( n*a*x^{(}n-1) - b*exp(x). The sequence, starting with (that particular) x_{0} and applying the iterative procedure x_{n+1} = G(x_{n}) converges rapidly to the zero z = 1.5196... of F(x).

Newton's procedure is a special iterative procedure (see Iterative.html ). By moving x_{0}, you can see that the initial x_{0} for the sequence converging to that root can be arbitrarily selected from the interval [1, 6.5]. But for values as big as x_{0} = 8.0 the convergence fails.