Let be a function with a stationary point at such that and

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

Problem

Let

f

be a function with a stationary point at

x=c

such that

f'(c)=0

and

f''(c)=0

. Which of the following statements is correct regarding the use of the second derivative test at

x=c

? (a)

f(c)

is a local minimum. (b) It gives no conclusion; further investigation is required. (c)

x=c

is a point of inflection. (d)

x=c

is not a stationary point.