Let be three times differentiable on with ,

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Let

f

be three times differentiable on

\mathbb R

with

f'(5)=0

f''(5)=0

, and

f'''(5)<0

. Which of the following statements about

x=5

is correct? (a)

f

has a local maximum at

x=5

. (b)

f

has a local minimum at

x=5

. (c)

f

has a point of inflection at

x=5

and neither a local maximum nor a local minimum. (d) The information given is insufficient to classify the critical point at

x=5