Approximating real functions which possess nnth derivatives of bounded variation and applications

The main aim of this paper is to provide an approximation for the function ff which possesses continuous derivatives up to the order n−1(n≥1)n−1(n≥1) and has the nnth derivative of bounded variation, in terms of the chord that connects its end points A=(a,f(a))A=(a,f(a)) and B=(b,f(b))B=(b,f(b)) and some more terms which depend on the values of the kk derivatives of the function taken at the end points aa and bb, where kk is between 1 and nn. Natural applications for some elementary functions such as the exponential and the logarithmic functions are given as well.