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Math Help - Linear Approximation

  1. #1
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    Linear Approximation

    Find the linear approximation to f(x) = sqrt(1-4x) at x=-2

    I keep getting (-2/3)*x +(13/3) as the answer, but it is wrong?
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  2. #2
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    Quote Originally Posted by Velvet Love View Post
    Find the linear approximation to f(x) = sqrt(1-4x) at x=-2

    I keep getting (-2/3)*x +(13/3) as the answer, but it is wrong?
    check your arithmetic ... I get

    y = -\frac{2}{3}x + \frac{5}{3}
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  3. #3
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    yes you took the derivative correctly, but it looks like something went wrong when you brought 3 over from the left hand side, or maybe when you multiplied through by -\frac{2}{3}
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  4. #4
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    Can you show me the steps? I do everything by the book, and i still get that answer.
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  5. #5
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    Quote Originally Posted by Velvet Love View Post
    Can you show me the steps? I do everything by the book, and i still get that answer.

    The equation of the tangent line is

    y-b=m(x-a)

    m is your derivative evaluated at a, which you did correctly, so what went wrong was solving for y after that, it's an error in your arithmetic

    y-3=-\frac{2}{3}(x-(-2))
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