First find the derivative:

By implicit differentiation:

Now, where is ? When

So put this into your original equation:

So ==> ==>

or ==> ==>

So the points where are and . (Both of these are points in the original equation.)

We do the same process to find where the vertical tangents are. Where is undefined? Where

So put this into your original equation:

Let

Then

For the "-" sign:

==> ==>

(I note that the "-" solution is not a point on the original equation.)

and

==> ==>

(I note that the "+" solution is not a point on the original equation.)

So the "-" sign in the z quadratic equation gives points for the vertical asymptote at and .

For the "+" sign:

==> ==>

which isn't real.

and

==> ==> .

So the "+" sign in the z quadratic equation gives points for the vertical asymptote at . I note that the "+" sign is not a solution of the original equation, so the vertical asymptote is at .

Overall this gives us vertical asymptotes at and .

-Dan