# Ch 15: Rate of Change in AP Calculus: Tutoring Solution

### About This Chapter

## How it works:

- Begin your assignment or other AP calculus work.
- Identify the rate of change concepts that you're stuck on.
- Find fun videos on the topics you need to understand.
- Press play, watch and learn!
- Complete the quizzes to test your understanding.
- As needed, submit a question to one of our instructors for personalized support.

## Who's it for?

This chapter of our AP calculus tutoring solution will benefit any student who is trying to learn about rate of change for AP calculus and earn better grades. This resource can help students including those who:

- Struggle with understanding velocity and slope, the Mean Value Theorem and Rolle's Theorem, derivatives or any other rate of change in AP calculus topic
- Have limited time for studying
- Want a cost effective way to supplement their math learning
- Prefer learning math visually
- Find themselves failing or close to failing their rate of change in AP calculus unit
- Cope with ADD or ADHD
- Want to get ahead in AP calculus
- Don't have access to their math teacher outside of class

## Why it works:

**Engaging Tutors:**We make learning about rate of change for AP calculus simple and fun.**Cost Efficient:**For less than 20% of the cost of a private tutor, you'll have unlimited access 24/7.**Consistent High Quality:**Unlike a live calculus tutor, these video lessons are thoroughly reviewed.**Convenient:**Imagine a tutor as portable as your laptop, tablet or smartphone. Learn about rate of change on the go!**Learn at Your Pace:**You can pause and rewatch lessons as often as you'd like, until you master the material.

## Learning Objectives

- Determine the rate of change using motion.
- Describe the relationship between slopes and the rate of change.
- Become familiar with the mean value theorem.
- Explain the relationship between Rolle's theorem and the mean value theorem.
- Define derivatives.
- Express derivatives as graphical representations.
- Discuss what it means to be differentiable.

### 1. Velocity and the Rate of Change

Running from your little sister or just window-shopping, your speed is just a measure of how fast you move, or how your position is changing over time. In this lesson, learn about how velocity is a rate of change.

### 2. Slopes and Rate of Change

If you throw a ball straight up, there will be a point when it stops moving for an instant before coming back down. Consider this as we study the rate of change of human cannonballs in this lesson.

### 3. 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.

### 4. 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.

### 5. Derivatives: The Formal Definition

The derivative defines calculus. In this lesson, learn how the derivative is related to the instantaneous rate of change with Super C, the cannonball man.

### 6. Derivatives: Graphical Representations

Take a graphical look at the definitive element of calculus: the derivative. The slope of a function is the derivative, as you will see in this lesson.

### 7. What It Means To Be 'Differentiable'

Lots of jets can go from zero to 300 mph quickly, but super-jets can do this instantaneously. In this lesson, learn what that means for differentiability.

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### Other Chapters

Other chapters within the AP Calculus AB & BC: Tutoring Solution course

- Functions in AP Calculus: Tutoring Solution
- Graphing and Functions in AP Calculus: Tutoring Solution
- Sequences and Series in AP Calculus: Tutoring Solution
- Limits in AP Calculus: Tutoring Solution
- Continuity in AP Calculus: Tutoring Solution
- Exponentials and Logarithms in AP Calculus: Tutoring Solution
- Exponents and Polynomials in AP Calculus: Tutoring Solution
- Applications of Derivatives in AP Calculus: Tutoring Solution
- AP Calculus - Derivatives Calculations & Rules: Tutoring Solution
- Differential Equations in AP Calculus: Tutoring Solution
- Area Under the Curve and Integrals in AP Calculus: Tutoring Solution
- AP Calculus - Graphing Derivatives & L'Hopital's Rule: Tutoring Solution
- AP Calculus - Integration: Tutoring Solution
- Integration Applications in AP Calculus: Tutoring Solution
- Geometry and Trigonometry in AP Calculus: Tutoring Solution
- How to Use Scientific Calculators for AP Calculus: Tutoring Solution