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Math Help - Linear Approximation

  1. #1
    Member
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    Linear Approximation

    Find the linear approximation, for...
     y=mx+b, to f(x) = \sqrt[3]{3x-1}
    at the point x=3

    Ok, so
    f(3)=2
    f'(x)=3x-1
    f'(3)=8
    now to solve for y=mx+b?..
    2=8(3)+b
    b=-22
    y=8x-22

    this is apparently wrong. What am I doing wrong here?
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  2. #2
    MHF Contributor Unknown008's Avatar
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    I think you got the wrong expression for f'(x)

    f(x) = (3x - 1)^{\frac13}

    f'(x) = \dfrac13 (3x-1)^{-\frac23} \cdot 3 = (3x-1)^{-\frac23} = \sqrt[3]{\dfrac{1}{(3x-1)^2}}
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