Posted by Stephanie on .
the curve: (x)(y^2)(x^3)(y)=6
(dy/dx)=(3(x^2)y(y^2))/(2xy(x^3))
a) find all points on the curve whose xcoordinate is 1 and write an equation for the tangent line of each of these points
b)find the xcoordinate of each point on the curve where the tangent line is vertical

Calculus 
drwls,
a) If x = 1, y^2 y 6 = 0
(y3)(y+2)  0
y = 3 or 2
b) Find the points where dy/dx = infinity
Those would be the places where the denominator of dy/dx = 0. x=0 is one such point. Any point where x^2 = 2y would be another, if there is such a point on the curve.