MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
A twice-differentiable function f satisfies f′′(c)=0 at x=c. Which of the following must also be true if x=c is an inflection point of f?
(a) The third derivative f′′′ satisfies f′′′(c)=0.
(b) The second derivative f′′ changes sign at x=c.
(c) The first derivative f′ satisfies f′(c)=0.
(d) The second derivative f′′ is positive on both sides of x=c.