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Differentiating Inverse Functions

AP Calculus AB· difficulty 3/5

Suppose f(1)=0f(1) = 0, f′(1)=5f'(1) = 5. Then (f−1)′(0)=(f^{-1})'(0) =

  • A

    00

  • B

    55

  • C

    Undefined

  • D

    15\tfrac{1}{5}

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Explanation

(f−1)′(0)=1/f′(f−1(0))=1/f′(1)=1/5(f^{-1})'(0) = 1/f'(f^{-1}(0)) = 1/f'(1) = 1/5.

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