TITLE: What does "$f\in C^2[a,b]$" mean?
QUESTION [12 upvotes]: What does this expression mean?
$$f\in C^2[a,b]$$
More specifically, I don't know what $C$ means.

REPLY [3 votes]: $f:[a,b]\to \mathbb{R}$ or $\to \mathbb{C}$. And both the first  and second derivatives of $f$ are continuous.