Let be differentiable on with for ,

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

Let

f

be differentiable on

(-4,6)

with

f'(x)>0

for

-4<x<2

f'(2)=0

, and

f'(x)<0

for

2<x<6

. Which of the following statements about

f

x=2

is true? (a)

f

has an inflection point at

x=2

(b) No conclusion can be drawn about relative extrema at

x=2

(c)

f

has a local maximum at

x=2

(d)

f

has a local minimum at

x=2