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“Non-strict” l’Hospital-type rules for monotonicity: intervals of constancy. (English) Zbl 1232.26008

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 \( r\).

MSC:

26A48 Monotonic functions, generalizations
26D10 Inequalities involving derivatives and differential and integral operators
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