**2.2 THE DERIVATIVE AT A POINT**

Average Rate of Change

Instantaneous Rate of Change: The Derivative

Visualizing the Derivative: Slope of Curve and Slope of Tangent

Estimating the Derivative

Computing the Derivative Algebraically

**2.3 THE DERIVATIVE FUNCTION**

The Derivative Function: Graphically

What Does the Derivative Tell Us Graphically?

The Derivative Function: Numerically

Improving Numerical Estimates

Derivative Function: From a Formula

Derivative of a Constant Function

Derivative of a Linear Function

Derivative of a Power Function

**2.4 INTERPRETATIONS OF THE DERIVATIVE**

An Alternative Notation for the Derivative

Using Units to Interpret the Derivative

**2.5 THE SECOND DERIVATIVE**

Second and Higher Derivatives

What Do Derivatives Tell Us?

Interpretation of the Second Derivative as a Rate of Change

Velocity and Acceleration

**2.6 DIFFERENTIABILITY**

What Does It Mean for a Function to Be Differentiable?

Some Non-differentiable Functions

Differentiability and Continuity