How do I find all points on a curve whose x coordinate is 1? Then, how do I write an equation for the tangent line at each of these points?
The curve is xy^2-x^3y=6
& I already have the derivative.
Plug in into the original equation to find the y values.
This can be easily factored. You will get two y values, which I will denote as and respectively.
This will give you the two points: and
Now, find the derivative [which you already did] and then plug these points into . Each point will create a different slope, and , respectively.
Now to find the equations of the tangents, use the point slope form of a line. You will have two equations:
Can you take it from here?