The derivative of a differentiable function satisfies ,
MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
The derivative of a differentiable function f satisfies f′(2.9)=−1.2, f′(3)=0, and f′(3.1)=0.8. It is also known that f′′(3)=0. Which of the following conclusions about f at x=3 is most accurate?
(a) The graph of f has a point of inflection but neither a maximum nor a minimum at x=3.
(b) No determination about relative extrema can be made from the given information.
(c) The graph of f has a relative minimum at x=3.
(d) The graph of f has a relative maximum at x=3.