MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation
Problem
Three twice-differentiable functions A, B, and C are graphed on the same axes (graphs not shown). The following observations are recorded.
• B is positive wherever A is increasing and negative wherever A is decreasing.
• C is positive wherever B is increasing and negative wherever B is decreasing.
• At x=4, A has an inflection point, and B has a relative minimum.
Which of the following identifications of A, B, and C is most consistent with these observations?
(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′