# Ch 33: Applications of Derivatives in Calculus

### About This Chapter

## Applications of Derivatives in Calculus - Chapter Summary

If you're looking for a way to study the applications of derivatives in calculus, you're in the right place. This comprehensive chapter includes short video lessons on a variety of derivative topics, such as the mean value theorem, linearization and the rules of differentiation. By the end of the chapter, you'll be able to:

- Explain the mean value theorem and Rolle's theorem
- Use linearization to estimate function values
- Find the roots of equations by applying Newton's method
- Differentiate complex functions with the chain rule
- Calculate derivatives using the rules of differentiation

Take the chapter's self-assessment quizzes to practice solving differentiation problems on your own. If you need any extra help with these concepts, feel free to reach out to our instructors with your questions. The chapter is accessible 24/7, and you can study whenever you have free time in your schedule.

### 1. What is the Mean Value Theorem?

Three people set off on a car trip. They all start at the same time and end at the same time. Learn what calculus says about how fast they traveled along the way as you study the Mean Value Theorem in this lesson.

### 2. Rolle's Theorem: A Special Case of the Mean Value Theorem

Super C, the human cannonball, is shot into the air at 35 mph, but his average vertical velocity is zero. In this lesson, you will use Rolle's theorem to explain what this means about Super C's flight.

### 3. How to Estimate Function Values Using Linearization

Sometimes landing on Mars isn't that easy. You might need to use linearization to estimate if you will crash into the planet, or miss it entirely. Learn how to do just that in this lesson.

### 4. How to Use Newton's Method to Find Roots of Equations

Finding the roots of equations usually requires the use of a calculator. However, in this lesson you'll use Newton's Method to find the root of any equation, even when you can't solve for it explicitly.

### 5. Using the Chain Rule to Differentiate Complex Functions

If you've ever seen a complicated function, this lesson is for you. Most functions that we want to differentiate are complicated functions, for which no single derivative rule will work. In this lesson, learn how to use the chain rule to simplify nesting equations.

### 6. Applying the Rules of Differentiation to Calculate Derivatives

In this lesson, we'll review common derivatives and their rules, including the product, quotient and chain rules. We'll also examine how to solve derivative problems through several examples.

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### Other Chapters

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