find slope of xy^2 - 2y + 4y^3 = 6 at point where y = 1

[xtrmk]

If y is a differentiable function of x, then the slope of the curve of xy^2 - 2y + 4y^3 = 6 at the point where y = 1 is?

I'm probably not understanding it because the wording but do I set the equation y = and then take the derivative? Then plug in y=1? Will the answer be in terms of x?

 

[pka]

Have you used implicit differentiation to find y’? That is step #1.
Have you found the x-value for y=1? That is step #2.
Then find the value of y’ for that value of x.