A differentiable function is defined on an open interval containing

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

Problem

A differentiable function

g

is defined on an open interval containing

x=5

. The derivative satisfies

g'(x)>0

for

x<5

and

g'(x)<0

for

x>5

. Which statement about

g

x=5

is true? (a)

g

has a relative minimum at

x=5

. (b)

g

has a relative maximum at

x=5

. (c)

g

has a point of inflection at

x=5

. (d)

g

is increasing at

x=5

because

g'(5)>0