How do you find the point on a line that has a vertical tangent?

Question

For example in parametrics...where you dont necessarily have strict functions. How do you find that vertical tangent out manually (instead of just looking at the graph on a calculator)?

Answer 1

a vertical tangent means infiite slope
so you see if df/dx = f '(x) = infinity for some x.

Answer 2

If you have parametric equations, recall that
dy/dx = (dy/dt)/(dx/dt). You will have a vertical tangent whereever dx/dt = 0.