function with continuous derivative
noun phraseUK /ˈfʌŋkʃən wɪð kənˈtɪnjuəs dɪˈrɪvətɪv/
US /ˈfʌŋkʃən wɪð kənˈtɪnjuəs dɪˈrɪvətɪv/
A function whose slope changes smoothly without any sudden jumps.
The curve is a function with continuous derivative, so it has no sharp corners.
OTHER MEANINGS
2. A function whose derivative exists and is itself a continuous function on its domain.
Every function with continuous derivative is differentiable, but not every differentiable function has a continuous derivative.
3. A map between smooth spaces whose first derivative varies continuously.
In differential geometry, a function with continuous derivative defines a smooth path.
4. A real-valued function on an interval that can be approximated smoothly by its tangent lines.
Because it is a function with continuous derivative, the tangent line moves gradually along the graph.