Curves A, B, and C are drawn on the same coordinate plane and have the following…
MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
Curves A, B, and C are drawn on the same coordinate plane and have the following characteristics.
• Curve A is decreasing on (−∞,−1), increasing on (−1,5), and decreasing on (5,∞). It attains a local minimum of −4 at x=−1 and a local maximum of 6 at x=5.
• Curve B is below the x-axis on (−∞,−1), above the axis on (−1,5), and below the axis on (5,∞). It crosses the x-axis at x=−1 and x=5. Curve B has a single local minimum at (2,0).
• Curve C crosses the x-axis at x=2, is positive on (−∞,2), and negative on (2,∞).
Exactly one of these curves is a twice-differentiable function f, and the other two are its first and second derivatives. Which of the following identifications is most consistent with the information above?
(a) A is f′, B is f′′, C is f
(b) A is f, B is f′′, C is f′
(c) A is f′′, B is f, C is f′
(d) A is f, B is f′, C is f′′