Consider a twice–differentiable function whose derivative is given by
MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
Consider a twice–differentiable function f whose derivative is given by f′(x)=(x−1)2(x+2). Which of the following statements must be true?
(a) f has a relative maximum at x=−2 and points of inflection at x=−1 and x=1.
(b) f has no relative extrema because f′(x) is always nonnegative.
(c) f has a relative minimum at x=−2 and points of inflection at x=−1 and x=1.
(d) f has a relative maximum at x=1 and is concave down for x>1.