Students will learn why all differentiable functions are continuous. Before attempting this section, students should know both limit definitions of a derivative, and the limit definition of a continuous function. They should also know the properties of limits.
Calculus I - Proof that Differentiability Implies Continuity by The Infinite Looper
Conclude by giving your students these challenges:
- Can you find the trick? by Mathy Mahdi
- Win or Lose? by NRICH
- Fruity Totals by NRICH
- 2008 AMC 8, Problem 10
- A Reflected Triangle