MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
Let f(x)=(x−2)(x+1)2 for all real x. Which of the following statements about the graph of an antiderivative of f′(x) is true?
(a) The graph has a local maximum at x=2 and a local minimum at x=−1.
(b) The graph has local minima at both x=−1 and x=2.
(c) The graph has a local minimum at x=2 and no local extremum at x=−1.
(d) The graph has a local maximum at x=−1 and no local extremum at x=2.