continuously differentiable function
nounA function whose slope changes smoothly without any sudden jumps.
The curve of a roller coaster track is a continuously differentiable function because it has no sharp corners.
OTHER MEANINGS
2. A function that is differentiable everywhere and whose derivative is itself a continuous function.
In calculus class, we proved that every continuously differentiable function is continuous.
3. A mathematical mapping belonging to the class C1, meaning both the function and its first derivative are continuous.
The engineer modeled the road profile as a continuously differentiable function to ensure a comfortable ride.
4. A real-valued function on an interval whose graph has a well-defined tangent line that varies continuously.
The student showed that the polynomial is a continuously differentiable function on the whole real line.