Unit 2: Differentiation: Definition and fundamental properties

Three Ways Graphs fail differentiability

Differentiability and Continuity

• if f(x) is differentiable at x = a, then f(x) must be continuous at x = a

• if f(x) is continuous at x = a, it does not imply that f(x) is differentiable at x = a

• In order to prove differentiability

1. Prove Continuity

2. Prove left handed limit of the derivative at x = a equals the right handed limit of the derivative at x = a

Resources / Example problems

• Study Guide

• Example Problems