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Math Help - Inverse Question: (Help before final exam)

  1. #1
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    Inverse Question: (Help before final exam)

    I have my calc final today and forget how to do problems like this:

    Let f(x) = 2x^2 (x is greater than or equal to 0) Find df^-1/dx at x=3

    I know there is a formula 1/(f' (f^-1(b)) I am having trouble figuring out how to compute this can someone please show me! Thanks!
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  2. #2
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    You can use this formula, or simply, you can find the inverse function itself and evaluate its derivative when x=3 ..
    We have f(x)=2x^2 with x\geq 0, so its a one-to-one function since its an increasing function ..
    Clearly, f^{-1}(x)=\sqrt{\frac{x}{2}}=\frac{1}{\sqrt{2}} \cdot \sqrt{x} ..

    Differentiate it, and evaluate its derivative at x=3 ..
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