AP Calculus ABhardmcq1 pt

A one-to-one differentiable function ff satisfies f(1)=4f(1)=4, f(2)=7f(2)=7, f(3)=9f(3)=9, f(1)=2f'(1)=2, f(2)=5f'(2)=5, and f(3)=11f'(3)=11. What is (f1)(7)(f^{-1})'(7)?

A.15\dfrac{1}{5}
B.55
C.12\dfrac{1}{2}
D.111\dfrac{1}{11}

Explanation

Core Concept

The value 7 is f(2)f(2), so f1(7)=2f^{-1}(7)=2. The formula gives (f1)(7)=1f(2)=15(f^{-1})'(7)=\frac{1}{f'(2)}=\frac{1}{5}.

Correct Answer

A15\dfrac{1}{5}

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