Almeida, Ricardo A mean value theorem for internal functions and an estimation for the differential mean point. (English) Zbl 1274.26081 Novi Sad J. Math. 38, No. 2, 57-64 (2008). Summary: We present several results about the mean value theorem (MVT) with techniques from nonstandard analysis. Using only the intermediate value theorem, we present a nonstandard proof of the MVT and 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 \(y\to x\). MSC: 26E35 Nonstandard analysis 26B05 Continuity and differentiation questions 46S20 Nonstandard functional analysis 46T20 Continuous and differentiable maps in nonlinear functional analysis Keywords:nonstandard analysis PDFBibTeX XMLCite \textit{R. Almeida}, Novi Sad J. Math. 38, No. 2, 57--64 (2008; Zbl 1274.26081)