Lesson: The Differentiability of a Function Mathematics

Students will be able to

• understand the definition of the differentiability of a function at a point,
• understand the definition of the differentiability of a function over an interval,
• understand the relationship between the differentiability and the continuity of a function,
• determine whether a given function is differentiable at a point (or over an interval),
• recognize and classify the cases where a function is not differentiable at a point, including
  • discontinuities,
  • corners,
  • cusps,
  • vertical tangents,
  • cases of oscillating behavior.