Implicit differentiation results in no x I believe I understand what to do until a point, but I'm looking for a way to wrap my head around the last step.
Curve:
$x+y^2-y=1$
I'm asked to find a) All points where a vertical tangent line occurs, b) All points where a horizontal tangent line occurs.
I can differentiate it, resulting in
$y'(x)=-\frac{1}{2y-1}$
There would be a horizontal asymptote as the function approaches infinity, therefore SOMETHING equals zero, and a vertical asymptote at .5.
What I can't understand is if those points I listed above would count as x's or y's, and how I could actually obtain the coordinates (x,y). I know I should plug in the result into the original equation, but, again, I don't understand the result.
Therefore, I don't understand the function itself since there is no x.
Any help is greatly appreciated, thank you! 

You may view this curve as the graph of some function by writing the equation in the form $$x = f(y).$$
There are methods for general implicit equations $F(x, y) = 0$ involving the gradient of $F$ but no such technique is required here.
