Let be a differentiable function with an inverse

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Let ff be a differentiable function with an inverse gg. Suppose ff is strictly decreasing and f′(2)=−4f'(2)=-4. Which of the following statements must be true? (a) g′(f(2))=−4g'(f(2))=-4 (b) g′(f(2))=14g'(f(2))=\dfrac14 (c) g′(f(2))=−14g'(f(2))=-\dfrac14 (d) g′(2)=−14g'(2)=-\dfrac14

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