Pinelis, Iosif “Non-strict” l’Hospital-type rules for monotonicity: intervals of constancy. (English) Zbl 1232.26008 JIPAM, J. Inequal. Pure Appl. Math. 8, No. 1, Paper No. 14, 8 p. (2007). Summary: Assuming that a “derivative” ratio \( r:=f/g\) of differentiable functions \( f\) and \( g\) is strictly monotonic (that is, \( r\) can switch at most once, from decrease to increase or vice versa. In the present paper, it is shown that, if \( r\) can have at most one maximal interval of constancy (m.i.c.); on the other hand, any one m.i.c. of a given derivative ratio \( r\). Cited in 12 Documents MSC: 26A48 Monotonic functions, generalizations 26D10 Inequalities involving derivatives and differential and integral operators Keywords:l’Hospital-type rules for monotonicity; intervals of constancy PDFBibTeX XMLCite \textit{I. Pinelis}, JIPAM, J. Inequal. Pure Appl. Math. 8, No. 1, Paper No. 14, 8 p. (2007; Zbl 1232.26008) Full Text: arXiv EuDML EMIS