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Math Help - tangent line

  1. #1
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    tangent line

    The slope of the tangent line to the curve at the point is: i got 0.040816326 but its wrong

    The equation of this tangent line can be written in the form where is:

    and where is:
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by wannous View Post
    The slope of the tangent line to the curve at the point is: i got 0.040816326 but its wrong

    The equation of this tangent line can be written in the form where is:

    and where is:
    Your answer is wrong because you forgot the minus sign. The derivative of \frac{2}{x} is -\frac{2}{x^2}. Plug in x=7 to get that m=-\frac{2}{49}.

    Spoiler:
    Use point slope form for the equation:

    y-\frac{2}{7}=-\frac{2}{49}(x-7) \implies y=-\frac{2}{49}x+\frac{4}{7}
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  3. #3
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    Quote Originally Posted by wannous View Post
    The slope of the tangent line to the curve at the point is: i got 0.040816326 but its wrong

    The equation of this tangent line can be written in the form where is:

    and where is:
    put away the calculator.

    the point of tangency is \left(7 , \frac{2}{7} \right)

    y = 2x^{-1}

    y' = -2x^{-2} = -\frac{2}{x^2}

    slope = y'(7) = -\frac{2}{7^2} = -\frac{2}{49}<br />

    now finish.
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