MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
Consider three continuous graphs—A, B, and C—that model a twice-differentiable function g and its first two derivatives.
• Graph A is always decreasing and concave down.
• Graph B crosses the x-axis at x=−2 and x=3, is below the axis on (−2,3), and above the axis elsewhere.
• Graph C is negative on (−∞,0), positive on (0,∞), and has a local minimum at x=0.
If exactly one of these graphs is g′′, which graph is it?
(a) C
(b) A
(c) None of the three
(d) B