Chapter 3: Applications of Differentiation
Course
MATH161 (Calculus I)
Overview
This chapter covers Applications of Differentiation from Stewart Calculus 9th Edition.
Each section contains:
- Skill breakdowns with learning objectives
- Practice problems at multiple difficulty levels
- Links to related skills and prerequisites
Sections
Section 3.1: Maximum and Minimum Values
| Skill | Description | Difficulty |
|---|---|---|
| Absolute and Local Extrema | Applications of Differentiation | Beginner |
| Absolute and Local Extreme Values | Applications of Differentiation | Intermediate |
| Absolute vs Local Extrema | Applications of Differentiation | Beginner |
| Critical Numbers | Applications of Differentiation | Intermediate |
| Fermat’s Theorem and Critical Numbers | Applications of Differentiation | Intermediate |
| The Closed Interval Method | Applications of Differentiation | Intermediate |
| The Extreme Value Theorem | Applications of Differentiation | Beginner |
Section 3.2: The Mean Value Theorem
| Skill | Description | Difficulty |
|---|---|---|
| Applications of MVT | Applications of Differentiation | Advanced |
| Product Rule | Differentiation Rules | Intermediate |
| Quotient Rule | Differentiation Rules | Intermediate |
| Rolle’s Theorem | Applications of Differentiation | Advanced |
| The Mean Value Theorem | Applications of Differentiation | Advanced |
Section 3.3: What Derivatives Tell Us about the Shape of a Graph
| Skill | Description | Difficulty |
|---|---|---|
| Concavity | Applications of Differentiation | Intermediate |
| Concavity and Inflection Points | Applications of Derivatives | Intermediate |
| Curve Sketching with Derivatives | Applications of Differentiation | Intermediate |
| The First Derivative Test | Applications of Differentiation | Intermediate |
| The Increasing/Decreasing Test | Applications of Differentiation | Intermediate |
| The Second Derivative Test | Applications of Differentiation | Intermediate |
Section 3.4: Limits at Infinity; Horizontal Asymptotes
| Skill | Description | Difficulty |
|---|---|---|
| Evaluating Limits of Rational Functions at Infinity | Limits | Intermediate |
| Horizontal Asymptotes | Applications of Differentiation | Intermediate |
| Infinite Limits at Infinity | Applications of Differentiation | Intermediate |
| Limits at Infinity | Applications of Differentiation | Intermediate |
| Limits at Infinity and Horizontal Asymptotes | Limits | Intermediate |
| Limits at Infinity: Rational Functions | Applications of Differentiation | Intermediate |
| Special Techniques for Limits at Infinity | Limits | Advanced |
Section 3.5: Summary of Curve Sketching
| Skill | Description | Difficulty |
|---|---|---|
| Complete Curve Sketching | Applications of Differentiation | Advanced |
| Guidelines for Sketching a Curve | Applications of Differentiation | Intermediate |
| Slant Asymptotes | Applications of Differentiation | Intermediate |
Section 3.6: Graphing with Calculus and Technology
| Skill | Description | Difficulty |
|---|---|---|
| Analyzing Function Families | Applications of Differentiation | Advanced |
| Graphing with Technology | Applications of Differentiation | Intermediate |
Section 3.7: Optimization Problems
| Skill | Description | Difficulty |
|---|---|---|
| Business and Economics Applications | Applications of Differentiation | Advanced |
| Business and Economics Optimization | Applications of Derivatives | Intermediate |
| Geometric Optimization | Applications of Differentiation | Advanced |
| Optimization Solution Methods | Applications of Derivatives | Intermediate |
| Setting Up Optimization Problems | Applications of Derivatives | Intermediate |
| Setting Up Optimization Problems | Applications of Differentiation | Advanced |
| Solving Optimization Problems | Applications of Differentiation | Advanced |
Section 3.8: Newton’s Method
| Skill | Description | Difficulty |
|---|---|---|
| Applying Newton’s Method | Applications of Differentiation | Advanced |
| Newton’s Method Formula | Applications of Differentiation | Advanced |
Section 3.9: Antiderivatives
| Skill | Description | Difficulty |
|---|---|---|
| Antiderivative Definition | Antiderivatives | Beginner |
| Antidifferentiation Formulas | Applications of Differentiation | Intermediate |
| Antidifferentiation Rules | Antiderivatives | Beginner |
| Initial Value Problems | Applications of Differentiation | Intermediate |
| Initial Value Problems | Antiderivatives | Intermediate |
| Rectilinear Motion | Applications of Differentiation | Intermediate |
| Rectilinear Motion from Antiderivatives | Antiderivatives | Intermediate |
| The Antiderivative of a Function | Applications of Differentiation | Intermediate |
Prerequisites
Before starting Chapter 3, review relevant prerequisite skills from earlier chapters.
| Previous | Up | Next |
|---|---|---|
| Chapter 2 | Home | Chapter 4 |