# Inflection point of non continuous or non differentiable function

• player1_1_1
In summary, the conversation discusses three functions and their potential inflection points. The first two functions do not meet the definition of an inflection point because they are not continuous at the point of potential inflection. The third function may qualify as an inflection point due to a change in concavity at the point, but it ultimately depends on the definition being used.

## Homework Statement

three functions:
$$y=\begin{cases}\arctan \frac{1}{x}\ x\neq0\\ 0\ x=0\end{cases}$$
$$y=\frac{1}{x}, y=|x^2-1|$$ and what about inflection point?

## The Attempt at a Solution

first function is concave on left of 0, convex on right, so from definition it should be inflection point, but its not continuous in this point, a function need to be continuous in this place or not?
in 2, $$x=0$$ should be inflection point, but its not in the domain, so is there inflection point?
in 3, function is continuous in $$x=1$$ but not differentiable, is there inflection point or not?

up,.

player1_1_1 said:

## Homework Statement

three functions:
$$y=\begin{cases}\arctan \frac{1}{x}\ x\neq0\\ 0\ x=0\end{cases}$$
$$y=\frac{1}{x}, y=|x^2-1|$$ and what about inflection point?

## The Attempt at a Solution

first function is concave on left of 0, convex on right, so from definition it should be inflection point, but its not continuous in this point, a function need to be continuous in this place or not?
in 2, $$x=0$$ should be inflection point, but its not in the domain, so is there inflection point?
in 3, function is continuous in $$x=1$$ but not differentiable, is there inflection point or not?

It probably depends on the definition your text gives. Most say it must be a point on the graph where the concavity changes. That would rule out the first two. I would say the third qualifies because of the change in concavity at the point. But your mileage may vary.

thx!