This is a rather for-the-sake-of-curiosity question. I have studied the points in which a function might not be differentiable, and the most basic three cases are:
Angular Point: when both left and right limits of the derivative in that point $p$ do exist (finite) but their values are different
Cusp: when both left and right limits of the derivative in that point $p$ are infinite and their signs are opposite
Inflection point at vertical tangent: when both left and right limits of the derivative in that point $p$ are infinite and of the same signs.
Now the question: are there USED OR MISUSED names for other types of non differentiable points? For example those cases:
When one of the limits exists finite and the other is infinite (no matter of the sign)
When one ot the limits exists finite and the other does not exist.
When one of the limits is infinite and the other does not exist.
I have found, for the first one, that it can be called a semi-cusp point.
I am interested in knowing if other names / types are known in literature.