Differentiability and Continuity
The relationship
Why differentiability implies continuity
When is a function NOT differentiable?
Corner (sharp turn)
- •
- •
- •
- •
Cusp
Vertical tangent
Decision flowchart
Left and right derivatives
Piecewise differentiability
Counterexample
The hierarchy
AP exam tips
- •
- •
- •
- •
Vocabulary
Unit 2 topics
Unit 2 overview12.1 Defining Average and Instantaneous Rates of Change22.2 Defining the Derivative of a Function32.3 Using Derivative Notation42.4 Estimating Derivatives at a Point52.5 Connecting Differentiability and Continuity62.6 Applying the Power Rule72.7 Derivative Rules: Constant, Sum, Difference, and Constant Multiple82.8 Connecting Derivative Rules with the Power Rule92.9 Derivatives of sin(x), cos(x), eˣ, and ln(x)102.10 The Product Rule112.11 The Quotient Rule122.12 Derivatives of tan(x), cot(x), sec(x), and csc(x)