Calculus
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

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.