Implicit differentiation help

[kristinamarie]

I have 2 questions on this assignment that I cant get done.
question 1 : 2x^3 + 3xy^2 - y^3 =0

Question 2: find the equation of the tangent to the curve xy^2 + 3x -3y=6. at the point (2,1)

After differentiation then do i set the function dy/dx to equal 0? and substitute for zero...find 2nd deriv then sub for 2 and 1?

[FWT]

question 1 : 2x^3 + 3xy^2 - y^3 =0

What are you supposed to do with this one?

Question 2: find the equation of the tangent to the curve xy^2 + 3x -3y=6. at the point (2,1)

After differentiation then do i set the function dy/dx to equal 0? and substitute for zero...find 2nd deriv then sub for 2 and 1?

For the second one, yeh, do the differentiation and solve for dy/dx. You have to get the deriv at (2,1), so plug the x and y in to get the number for dy/dx. This is y our slope for the tangent. Then do the point-slope thing to get your tangent line at the point.