A twice-differentiable function satisfies and

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

Problem

A twice-differentiable function

g

satisfies

g'(4)=0

and

g''(4)<0

. Which statement best describes the behavior of

g

x=4

? (a)

g

has a local minimum at

x=4

(the graph is concave up). (b)

g

has a local maximum at

x=4

(the graph is concave down). (c)

g

has a point of inflection at

x=4

(the concavity changes). (d) The given information is insufficient to determine the local behavior at

x=4

(more analysis is needed).