What does "$f\in C^2[a,b]$" mean?
What does this expression mean?
$$f\in C^2[a,b]$$
More specifically, I don't know what $C$ means.
$\endgroup$ 12 Answers
$\begingroup$$f∈C^2[a,b]$ means that $f : [a,b] \rightarrow \mathbb{R}$ is a function that is twice differentiable with each derivative continuous. That is, $f'$ and $f''$ both exist and are both continuous.
$C^0$ means the function is continuous, $C^1$ means the first derivative is continuous, $C^2$ means the second derivative is continuous, In general, $C^n$ means the $n^{th}$ derivative is continuous.
$\endgroup$ 5 $\begingroup$$f:[a,b]\to \mathbb{R}$ or $\to \mathbb{C}$. And both the first and second derivatives of $f$ are continuous.
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