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Math Help - calculus- finding points

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    calculus- finding points

    Consider the curve given by y^2 = 2 + xy.

    It's derivative is y/(2y-x)

    Find all points (x,y) on the curve where the line tangent to the curve has slope 1/2.

    Thanks
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Mr_Green View Post
    Consider the curve given by y^2 = 2 + xy.

    It's derivative is y/(2y-x)

    Find all points (x,y) on the curve where the line tangent to the curve has slope 1/2.

    Thanks
    set the derivative = 1/2 and solve for the corresponding x's and y's
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    .5 = y / (2y-x)

    how do i solve for this?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Mr_Green View Post
    .5 = y / (2y-x)

    how do i solve for this?
    you can begin by multiplying both sides by (2y - x)
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    Quote Originally Posted by Mr_Green View Post
    .5 = y / (2y-x)

    how do i solve for this?
    \frac{1}{2} = \frac{y}{2y - x}

    2y - x = 2y

    x = 0

    So this is true for all points on the curve (0, y) such that x \neq 2y.

    (You're in Calculus and you can't solve this???)

    -Dan
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