# find all vertical tangent lines of a curve

• Oct 3rd 2010, 09:23 PM
mwilks
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
• Oct 4th 2010, 02:30 AM
mr fantastic
Quote:

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.
• Oct 4th 2010, 03:59 AM
HallsofIvy
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?