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## Homework Statement

Consider the curve given by xy^2 - x^3y = 6

a. Find the derivative

b. Find all points on the curve whose x-coordinate is 1, and write an equation for the tangent line at each of these points.

c. Find the x-coordinate of each point on the curve where the tangent line is vertical/

## Homework Equations

xy^2 - xy^3 = 6

## The Attempt at a Solution

so i started with a and found the derivative to be y' = (3x^2*y - y^2)/(2xy - x^3) which was correct so no problems there

then i started b by plugging 1 for x into the original equation to get my y values which came out to be 3 and -2

then i plugged then into my equation for the derivative separately and found the derivative for 3 to be undefined and the derivative for -2 to be 2

i figured therefore there couldn't be any tangent equation for the y value of 3 so i used 2 and got the tangent to be y = 2(x-1)+2

im not sure everything after the derivative is correct

for part c i know that the equation for the tangent line has to just be straight line where it is just x = to a number but i don't know how to find that