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Differentiating Inverse Functions

AP Calculus AB· difficulty 4/5

If f(x)=x3+xf(x) = x^3 + x and gg is its inverse, then g′(2)g'(2) equals

  • A

    12\frac{1}{2}

  • B

    44

  • C

    14\frac{1}{4}

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  • D

    22

Explanation

f(1)=2f(1) = 2, so g(2)=1g(2)=1. g′(2)=1/f′(1)=1/(3+1)=1/4g'(2) = 1/f'(1) = 1/(3+1) = 1/4.

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