At a point , a differentiable function satisfies for . Which of the following is true…

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

Problem

At a point

x=c

, a differentiable function

f

satisfies

f'(x)<0

for

x<c

and

f'(x)>0

for

x>c

. Which of the following is true about

f

x=c

? (a)

f(c)

is neither a maximum nor a minimum. (b)

f(c)

is a local minimum. (c)

f(c)

is a local maximum. (d)

f(c)

must be a point of inflection.