# How do you find the points where the graph of #y^2+2y=4x^3−16x−1# is the tangent line vertical?

##### 1 Answer

The coordinates of the points that have vertical tangents are at

#### Explanation:

If

Then by implicit differentiation we have

Now we can solve for (dy)/(dx).

The tangent line will be vertical when

So the tangent line will be vertical when

Now we need to calculate the

This equation has three solutions. They are

Of course, looking at an actual plot of our relation (this is NOT a function) confirms that we have the correct answer.