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Differentiability & Continuity

Understanding the relationship between differentiability & continuity.

Mapped to AP College Board # FUN-2, FUN-2.A, FUN-2.A.1, FUN-2.A.2

Recognizing that a function’s derivative may also be a function allows us to develop knowledge about the related behaviors of both. Explain the relationship between differentiability and continuity. If a function is differentiable at a point, then it is continuous at that point. In particular, if a point is not in the domain of f, then it is not in the domain of f’. A continuous function may fail to be differentiable at a point in its domain.