The aim of this paper is to describe a non-parametric technique as a means of estimating the instantaneous force of mortality which serves as the underlying concept in modeling the future lifetime. It relies heavily on the analytic properties of life table survival functions 𝒍𝒙+𝒕. The specific objective of the study is to estimate the force of mortality using the Taylor series expansion to a desired degree of accuracy. The estimation of the continuous death probabilities has aroused keen research interest in mortality literature on life assurance practice. However, the estimation of 𝝁𝒙 involves a model dependent on deep knowledge of differencing and differential equation of first order. The suggested method of approximation with limiting optimal properties is the Newton’s forward difference model. Initiating Newton’s process is an important level in terms of theoretical work which produces parallel results of great impact in the study of mortality functions. The paper starts from an assumption that 𝒍𝒙 function follows a polynomial of least degree and hence gives an answer to a simple model which overcomes points of singularity. Keywords: polynomials, contingency, analyticity, basis, differential, mortality, modeling