A mean value theorem for internal functions and an estimation for the diifferential mean point

Abstract

In this paper we present several results about the mean value theorem (MVT) with nonstandard analysis techniques. Using only the intermediate value theo- rem, we present a nonstandard proof of the MVT. In the next section we extend the MVT for internal SU-di erentiable functions. In the end we shall discuss the location of the di erential mean point c in the segment [x; y], as y - x.