A differentiable function is strictly decreasing on an interval so that for every
MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions
Problem
A differentiable function p is strictly decreasing on an interval I so that p′(x)<0 for every x∈I. Which statement about (p−1)′(y) for y∈p(I) is most accurate?
(a) (p−1)′(y) is positive for all such y.
(b) (p−1)′(y) is negative when p′(x)<−1 and positive when −1<p′(x)<0.},{
(c) (p−1)′(y) is negative for all such y.
(d) The sign of (p−1)′(y) varies with y and cannot be determined from the given information.