# Inflection point of non continuous or non differentiable function

 P: 118 1. The problem statement, all variables and given/known data 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? 3. 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?
 Quote by player1_1_1 1. The problem statement, all variables and given/known data 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? 3. 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?