Let be a twice-differentiable function whose first derivative satisfies exactly at and
MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
Let p be a twice-differentiable function whose first derivative satisfies p′(x)=0 exactly at x=−3 and x=2. Unlabeled graphs U, V, W are known to be p, p′, and p′′ in some order.
• Graph U is positive on (−∞,−3), negative on (−3,2), and positive on (2,∞).
• Graph V is increasing on (−∞,−3), decreasing on (−3,2), increasing on (2,∞), and has horizontal tangents at x=−3 and x=2.
• Graph W is negative on (−3,2) and positive on the intervals (−∞,−3) and (2,∞).
Which assignment of graphs to p, p′, and p′′ is most consistent with this information?
(a) U is p, V is p′, W is p′′
(b) U is p′′, V is p, W is p′
(c) U is p′, V is p′′, W is p
(d) U is p, V is p′′, W is p′