Continuity and differentiability are fundamental concepts in calculus. Continuity refers to a function being unbroken or uninterrupted across its domain, meaning the function's graph can be drawn without lifting the pencil. Differentiability, on the other hand, means that a function has a derivative at every point in its domain, implying it has a defined slope that can change from point to point.

https://en.wikipedia.org/wiki/Differentiable_function