Converging Newton’s Method With An Inflection Point of A Function

For long periods of time, mathematics researchers struggled in obtaining the appropriate starting point when implementing root finding methods, and one of the most famous and applicable is Newton’s method. This iterative method produces sequence that converges to a desired solution with the assumption that the starting point is close enough to a solution. The word “close enough” indicates that we actually do not have any idea how close the initial point needed so that this point can bring into a convergent iteration. This paper comes to answer that question through analyzing the relationship between inflection points of one-dimensional non-linear function with the convergence of Newton’s method. Our purpose is to illustrate that the neighborhood of an inflection point of a function never fails to bring the Newton’s method convergent to a desired solution