Thread: find all vertical tangent lines of a curve

1. 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

2. Originally Posted by mwilks
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.

3. 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?