EDB — 2D0

[2D0]Let in the following \(A⊆ ℝ\) be an open set.

By saying that \(f:A→ℝ\) is differentiable we mean differentiable at any point.

Recall that, given \(k≥ 1\) integer, \(f\) is of class \(C^ k\) if \(f\) is differentiable \(k\)-times and the k-th derivative \(f^{(k)}\) is continuous; and \(f\) is of class \(C^∞\) if \(f\) is differentiable infinitely many times. (Sometimes we may write \(f∈ C^ k\) to signify that \(f\) is of class \(C^ k\), and \(f∈ C^∞\) if is of class \(C^∞\).)