How to determine from the graph of a function whether it is possible to draw a tangent, not parallel to the y-axis, to a particular point of it?

Question

Mathematics

I understand the concept of derivative. I realized that it is possible to find out whether a function is differentiable at a particular point according to the graph, if you know if there is a tangent to this point that is not parallel to the y-axis, but I did not understand how you can visually understand whether such a thing exists.

Answer 1

If it is clear that the function goes to infinity, then, of course, the tangent will tend to the vertical axis.
If the function is piecewise, then the derivative will not exist at the junction points of the pieces, but there will be left-hand and right-hand limits.