Written by the Fiveable Content Team • Last updated September 2025
Verified for the 2026 exam
Verified for the 2026 exam•Written by the Fiveable Content Team • Last updated September 2025
Definition
In calculus, smooth refers to functions that are continuous and have no sharp corners or breaks in their graph. They exhibit gradual changes and have no abrupt changes in direction.
A continuous function has no gaps, jumps, or holes in its graph. It can be drawn without lifting your pencil from the paper. It's like drawing an unbroken line without interruptions.
A differentiable function is one that has derivatives at every point within its domain. It means that you can find the slope (rate of change) of the function at any given point using calculus techniques.
Concave Up/Down: Concave up refers to functions that curve upward like a smiley face, while concave down refers to functions that curve downward like a frown. These terms describe the shape and curvature of graphs for certain types of functions.