Applied Calculus 5th Edition

Chapter Two

RATE OF CHANGE: THE DERIVATIVE

Contents

2.1 Instantaneous Rate of Change

Instantaneous Velocity

Defining Instantaneous Velocity Using the Idea of a Limit

Instantaneous Rate of Change

The Derivative at a Point

Visualizing the Derivative: Slope of the Graph and Slope of the Tangent Line

Estimating the Derivative of a Function Given Numerically

2.2 The Derivative Function

Finding the Derivative of a Function Given Graphically

What Does the Derivative Tell Us Graphically?

Estimating the Derivative of a Function Given Numerically

Improving Numerical Estimates

Finding the Derivative of a Function Given by a Formula

2.3 Interpretations of the Derivative

An Alternative Notation for the Derivative

Using Units to Interpret the Derivative

Using the Derivative to Estimate Values of a Function

Relative Rate of Change

2.4 The Second Derivative

What Does the Second Derivative Tell Us?

Interpretation of the Second Derivative as a Rate of Change

2.5 Marginal Cost and Revenue

Graphs of Cost and Revenue Functions

Marginal Analysis

REVIEW PROBLEMS

STRENGTHEN YOUR UNDERSTANDING

PROJECTS: Estimating Temperature of a Yam; Temperature and Illumination; Chlorofluorocarbons in the Atmosphere

Focus on Theory

Limits, Continuity, and the Definition of the Derivative

Definition of the Derivative Using Average Rates

The Idea of a Limit

Continuity

Using the Definition to Calculate Derivatives

2.1 ...