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-   -   Show that 3x^2-y^2+xy=4 is equal to y=2x when the gradient of the tangent is 8/3 (https://www.askmehelpdesk.com/showthread.php?t=570289)

  • Apr 14, 2011, 09:16 AM
    natardy
    show that 3x^2-y^2+xy=4 is equal to y=2x when the gradient of the tangent is 8/3
    Pure mathematics/module 1/implicit differntiation
  • Apr 14, 2011, 10:25 AM
    galactus

    Implicitly differentiate



    to get y'.

    Set the result = to 8/3 and solve for y.
  • May 31, 2011, 06:59 PM
    dvmohanrao
    3x^2-y^2+xy=4

    differentiate implicitly

    6x - 2y y ' + x y ' + y = 0

    y ' (2y - x) = 6x + y

    y ' = (6x + y)/(2y - x)

    since gradient is 8/3

    => (6x + y)/(2y - x) = 8/3

    => 18x + 3y = 16y - 8x

    => 13y = 26x

    => y = 2x

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