The function is twice differentiable for all real numbers
MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
The function q is twice differentiable for all real numbers. Its derivative satisfies q′(−1)=0 and q′(3)=0. Furthermore, q′′(−1)=5 and q′′(3)=−2. Which of the following correctly describes the nature of each critical point?
(a) q(−1) is a local maximum, and q(3) is a local maximum.
(b) q(−1) is a local minimum, and q(3) is a local maximum.
(c) q(−1) is a local maximum, and q(3) is a local minimum.
(d) q(−1) is a local minimum, and q(3) is a local minimum.