MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
At x=1 three unlabeled differentiable curves M, N, and P exhibit the following local behavior.
• Curve P has a horizontal tangent and changes from increasing to decreasing.
• Curve M crosses the x-axis, changing from positive values to negative values.
• Curve N is below the x-axis and decreasing.
Which identification of M, N, and P as f, f′, and f′′ is most consistent with this information?
(a) M is f, N is f′, P is f′′
(b) M is f, N is f′′, P is f′
(c) M is f′, N is f′′, P is f
(d) M is f′, N is f, P is f′′