Volume 3,  Issue 1, 2002

Article 5

L'HOSPITAL TYPE RULES FOR MONOTONICITY, WITH APPLICATIONS

IOSIF PINELIS

DEPARTMENT OF MATHEMATICAL SCIENCES, 
MICHIGAN TECHNOLOGICAL UNIVERSITY, 
HOUGHTON, MI 49931, USA
E-Mail: ipinelis@mtu.edu

Received 29 January, 2001; Accepted 11 August, 2001.
Communicated by: F. Qi

ABSTRACT.    Let $ f\;$ and $ g\;$ be differentiable functions on an interval $ (a,b)$, and let the derivative $ g^{\prime}\;$ be positive on $ (a,b)$. The main result of the paper implies that, if $ f(a+)=g(a+)=0\;$ and $ \dfrac{f^{\prime}}{g^{\prime}}\;$ is increasing on $ (a,b)$ , then $ \dfrac{f}{g}\;$ is increasing on $ (a,b)$ .
Key words:
L'Hospital's Rule, Monotonicity, Information Inequalities

2000 Mathematics Subject Classification:
26A48, 26D10, 26D07, 60E15, 62B10, 94A17.

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