Could someone please help with this: Find the coordinates of the point in the first quadrant at which the tangent line to the curve (x)^3-xy+(y)^3 =0 is parallel to the y axis.

Question

phi · Answer

Here is what the curve looks like.

phi · Answer

I would find dy/dx  and solve for when it is "undefined"  i.e. has infinite slope and thus is parallel to the y-axis.

To find dy/dx, use implicit differentiation.

phi · Answer

Here is a Khan video that shows how to do implicit differentiation https://www.khanacademy.org/math/differential-calculus/taking-derivatives/implicit_differentiation/v/implicit-differentiation-1

phi · Answer

Can you post how far you got with this problem ?