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  Volume 3, Issue 1, Article 5
 
L'Hospital Type Rules for Monotonicity, with Applications
    Authors: Iosif Pinelis,  
    Keywords: L'Hospital's Rule, Monotonicity, Information Inequalities  
    Date Received: 29/01/01  
    Date Accepted: 11/08/01  
    Subject Codes:

26A48,26D10,26D07,60E15,62B10,94A17.

  
    Editors: Feng 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)$ .

         
       
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