Find the equation of the tangent line to the graph of 3y − y^3 = 2x at the point (−1,2)

Question

Find the equation of the tangent line to the graph of 3y − y^3 = 2x at the point (−1,2)

Answer 1

Differentiate the equation implicitly to get dy/dx=(2/[3(1-y^2)].

When y=2 the slope is 2/[3(1-4)]=-2/9

-2/9=(y-2)/(x+1)

You can "massage" this last equation into any needed form.

Please note that I did graph the equation and the result which appears to be correct.