MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation
Problem
Three unlabeled graphs—P, Q, and R—describe differentiable functions on the interval −4<x<4.
• Graph P is increasing for x<0 and decreasing for x>0, has a horizontal tangent at x=0, and is concave down everywhere.
• Graph Q is negative for x<0, positive for x>0, and increasing everywhere. It has a point of inflection at x=0.
• Graph R is positive everywhere, decreasing for x<0 and increasing for x>0, and attains a minimum at x=0.
Assuming the three graphs represent f, f′, and f′′ for the same function f, which graph must be f′?
(a) P
(b) Q
(c) R
(d) Insufficient information to determine