For a twice differentiable function

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

Problem

f

, suppose

f'(c)=0

and

f''(c)=0

. Which one of the following statements correctly describes

x=c

? (a)

x=c

is definitely a point of inflection of

f

. (b)

x=c

is a local extremum; the nature can be decided from the sign of

f'''(c)

. (c) The second derivative test is inconclusive and the sign change of

f'(x)

around

c

must be examined. (d)

x=c

is definitely a local minimum of

f