A question about inflection point Does the function
$$
f(x)=
\begin{cases}
x^2   & x\leq1\\
2-x^2 & x>1
\end{cases}
$$
has an inflection point at $x=1$, or it hasn't because $f$ isn't differentiable at $x=1$? Thanks! 

In an inflection point need to exist a tangent line to the graph of the function, which in our case says that $f$ must be differentiable.
Thus, $(1,1)$ is not inflection point. 
