For a differentiable function with

MATHEMATICS · Subjective · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

For a differentiable function

R(x)=\dfrac{f(x)}{g(x)}

with

g(x)\neq 0

, describe the necessary condition that must hold at an interior point

x=c

where

R

attains a local extremum, and briefly explain why this condition is required.