A twice-differentiable function satisfies ,

MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

A twice-differentiable function

f

satisfies

f(2)=5

f'(2)=0

, and

f''(2)<0

. (a) Describe the concavity of the graph of

f

x=2

and explain how the value of

f''(2)

supports your conclusion. (b) Determine whether

x=2

corresponds to a local maximum, a local minimum, or neither for

f

. Provide a clear justification based on the information given.