Generalized fraction rules for monotonicity with higher antiderivatives and derivatives

preprint2022arXivOpen access

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'Hôpital rule for monotonicity, which we then extend to high order antiderivatives and derivatives, respectively.

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