Generalized fraction rules for monotonicity with higher antiderivatives and derivatives

TL;DR

This paper extends the classic fraction rules for monotonicity, such as Gromov's theorem and L'Hôpital's rule, to higher-order derivatives and antiderivatives, broadening their applicability.

Contribution

It introduces generalized versions of fraction rules for monotonicity involving higher-order derivatives and integrals, expanding the theoretical framework.

Findings

Extended monotonicity rules to higher derivatives and integrals

Unified approach for derivatives and antiderivatives in monotonicity

Potential applications in advanced calculus and analysis

Abstract

We first introduce the generic versions of the fraction rules for monotonicity, i.e. the one that involves integrals known as the Gromov theorem and the other that involves derivatives known as L'H\^opital rule for monotonicity, which we then extend to high order antiderivatives and derivatives, respectively.