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

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