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

Ricardo Almeida

We present several results about the mean value theorem (MVT) with nonstandard analysis techniques. Using only the intermediate value theorem, we present a nonstandard proof of the MVT. In the next section we extend the MVT for internal SU-differentiable functions. In the end we discuss the location of the differential mean point $c$ in the segment $[x,y]$, as $y\to x$