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.

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- November 9th 2008, 02:10 PM #1

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- November 9th 2008, 02:26 PM #2
To answer the first question:

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:

and

Can you take it from here?

--Chris

- November 9th 2008, 02:52 PM #3

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