Optimal choice of linear interval extension (Q1122944)

To get more accurate interval extension is an important problem in interval analysis. It is known that the choice of the formula is very important for this aim. Examination of this topic can be found for instance in the book of \textit{H. Ratschek} and \textit{J. Rokne} [Computer methods for the range of functions (1984; Zbl 0584.65019)]. In this paper the optimal choice of linear interval extension \(F_ 1(x)=f(c)+f'(X)(X- c)\) is investigated by means of c. One only needs to calculate function values at two particular points to find the optimal interval extension.