Definition:Continuously Differentiable/Real Function/Open Interval

Definition

Let $I\subset\R$ be an open interval.

Then $f$ is continuously differentiable on $I$ if and only if $f$ is differentiable on $I$ and its derivative is continuous on $I$.

Sources

• 2017: Amol Sasane: A Friendly Approach to Functional Analysis ... (previous) ... (next): Chapter $1.1$: Normed and Banach spaces. Vector Spaces