But I have read that a cusp is when the limit of the first derivative must tend to $+\infty$ when approaching the point from one direction and $-\infty$ when from the other. In this case it tends to $+1$ and $-1$ which should mean that it does not have a cusp here and does not fall into one of the non differentiable categories.

2018年2月5日 · I've seen many times the terms like "cusp" and "corner" in the calculus books but I want a formal and rigorous definition for it .

2016年7月21日 · For my calculus exam, I need to be able to identify if a function is indifferentiable at any point without a graph. I thought this would be rather simple, but I messed up on the question x^(2/3) because I did not realize it had a "cusp" at x = 0. How would I identify, or look for cusps based on the formula of a function, without graphing it?

2017年9月14日 · Cusp: where the slope of the tangent line changed from -infinity to +infinity (or the other way around) Corner: left-sided and right-sided derivatives are different. And I saw a problem which was asking if there is a corner or a cusp given a graph. The graph looked like: f(x)=-x, if x<0 =sqrt(x), if x>=0

Side limits of a function with a cusp (does the limit exist at the cusp? is it it differentiable at the cusp?) Hot Network Questions Simple Java program to aggregate lines of a text file

2015年11月11日 · Can cusps be considered points of inflection? I'm getting conflicting information but my thought process is that cusps cannot be points of inflection? Can points of inflection exist when there is a

2014年12月16日 · In the calculus book from which I teach (Calculus ... A cusp is where the one-sided derivatives tend to ...

2017年9月26日 · I would classify this as a corner. This is because "corners" and "cusps" are usually properties of the graph, rather than the function, and they are invariant by rigid movement of the plane. (And if you rota

2019年6月6日 · I seem to recall from one of my Calculus lectures that a function with a cusp on its graph does not have a limit at the cusp because the side limits are different. This in turn means that the function is not differentiable at the cusp.

2021年10月11日 · We know that a derivative fails at cusp or corner. As we know a corner is where you have two distinct tangent lines and a cusp is where you have one tangent line which is vertical. I realized that a cusp and corner can have infinitely many tangent lines. See the image below of what I mean. I draw vertical lines at the corner and cusp.