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Math Help - find all vertical tangent lines of a curve

  1. #1
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    find all vertical tangent lines of a curve

    curve : xy^2 - x^3y = 6
    derivative : (3x^2y - y^2) / (2xy - x^3)
    question : find the x coordinate of each point on the curve where the tangent line is vertical.

    i can find derivatives and stuff but i dont know how to answer this question. your a genius if you can figure this one out! thanks a lot in advance
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  2. #2
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    Quote Originally Posted by mwilks View Post
    curve : xy^2 - x^3y = 6
    derivative : (3x^2y - y^2) / (2xy - x^3)
    question : find the x coordinate of each point on the curve where the tangent line is vertical.

    i can find derivatives and stuff but i dont know how to answer this question. your a genius if you can figure this one out! thanks a lot in advance
    Solve 2xy - x^3 = 0 subject to xy^2 - x^3y = 6.
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  3. #3
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    You don't have to be a genius (although mr. fantastic certainly is!), you just have to know that a vertical line has "infinite" slope.

    What is the slope of a horizontal line? What is the relationship between slopes of lines that are perpendicular?
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