The derivative of a continuous function satisfies for

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

Problem

The derivative of a continuous function

g

satisfies

g'(x) > 0

for

x < 2

and

g'(x) < 0

for

x > 2

. What can you conclude about

x = 2

? (a)

x = 2\text{ is a point of inflection}

(b)

\text{No conclusion about extrema can be drawn}

(c)

g(2)\text{ is a local maximum}

(d)

g(2)\text{ is a local minimum}