I am trying to find examples of functions that are in $C^2(\mathbb{R})$ but not in $C^3(\mathbb{R})$. I am also wondering about $C^2[0,1]$ and $C^3[0,1]$.
If I am not mistaken about the definitions, a function is said to be in $C^p(A)$ if it is a real-valued function with the set $A$ as its domain and its $p$-th derivative being defined on all of $A$ and continuous.
Thanks!