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2.4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist

Syllabus
2020
Topic
2.4
Level
—

Learning objectives

—FUN-2.A—Explain the relationship between differentiability and continuity• FUN-2.A Explain the relationship between differentiability and continuity.• FUN-2.A.1 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 '.• FUN-2.A.2 A continuous function may fail to be differentiable at a point in its domain.• Enduring understanding FUN-2: Recognizing that a function’s derivative may also be a function allows us to develop knowledge about the related behaviors of both.

FUN-2.A—Explain the relationship between differentiability and continuity

  • FUN-2.A Explain the relationship between differentiability and continuity.
  • FUN-2.A.1 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 '.
  • FUN-2.A.2 A continuous function may fail to be differentiable at a point in its domain.
  • Enduring understanding FUN-2: Recognizing that a function’s derivative may also be a function allows us to develop knowledge about the related behaviors of both.