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.