A twice-differentiable function satisfies and

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

Problem

A twice-differentiable function

f

satisfies

f'(1)=0

and

f'(4)=0

. Additional information is

f''(1)=-3

and

f''(4)=5

. Which of the following statements about

f

is true? (a)

f

has a local minimum at

x=1

and a local maximum at

x=4

. (b)

f

has inflection points at both

x=1

and

x=4

. (c)

f

has a local maximum at

x=1

and a local minimum at

x=4

. (d)

f

has a local maximum at

x=1

and an inflection point at

x=4