Suppose is differentiable on the real line and satisfies for

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

Problem

Suppose

g

is differentiable on the real line and satisfies

g'(x)<0

for

x<3

and

g'(x)>0

for

x>3

. Which statement describes the behavior of

g

x=3

? (a)

g

has no local extremum at

x=3

because

g'

changes sign. (b)

g

has a point of inflection at

x=3

. (c)

g

has a local minimum at

x=3

. (d)

g

has a local maximum at

x=3