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Math Help - Help with differentiation..

  1. #1
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    Help with differentiation..

    Show that the equation of the tangent to y = 1 / x at the point for which x = p is p^2y + x = 2p. At what point on the curve is the equation of the tangent 9y + x + 6 = 0?

    Differentiating:
    f'(x) = -1/x^2

    Then, the gradient is:
    f'(p) = -1 / p^2

    Shouldn't the equation be worked as follow? It's not working..
     y - (1 / p) = -p^-2(x - p)
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  2. #2
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    Quote Originally Posted by struck View Post
    Show that the equation of the tangent to y = 1 / x at the point for which x = p is p^2y + x = 2p. At what point on the curve is the equation of the tangent 9y + x + 6 = 0?

    Differentiating:
    f'(x) = -1/x^2

    Then, the gradient is:
    f'(p) = -1 / p^2

    Shouldn't the equation be worked as follow? It's not working..
     y - (1 / p) = -p^-2(x - p)
    It's not working.. ???

    y - \dfrac1p = -\dfrac1{p^2}(x - p) Multiply the equation by p^2

    p^2 y -p = -x+p Rearrange the equation:

    p^2y + x = 2p
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