A differentiable function has derivative values satisfying at and

MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

A differentiable function

g

has derivative values satisfying

g'(x)=0

x=-2

and

x=4

g'(x)>0

for

-2<x<4

, and

g'(x)<0

for

x<-2

as well as

x>4

. Determine whether

g

has a local maximum, a local minimum, or neither at the following points: (i)

x=-2

(ii)

x=4