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Differentiating Inverse Functions

AP Calculus AB· difficulty 3/5

If ff has inverse f−1f^{-1} and f(2)=5f(2) = 5, f′(2)=4f'(2) = 4, then (f−1)′(5)=(f^{-1})'(5) =

  • A

    14\tfrac{1}{4}

    check_circle
  • B

    44

  • C

    15\tfrac{1}{5}

  • D

    55

Explanation

(f−1)′(b)=1/f′(a)(f^{-1})'(b) = 1/f'(a) where f(a)=bf(a) = b. Here 1/f′(2)=1/41/f'(2) = 1/4.

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