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Ch 6: Rate of Change: Tutoring Solution

About This Chapter

The Rate of Change chapter of this Calculus Tutoring Solution is a flexible and affordable path to learning about rate of change. These simple and fun video lessons are each about five minutes long, and they teach all of the theorems and derivatives involving rate of change required in a typical calculus course.

How it works:

  • Begin your assignment or other 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 calculus tutoring solution will benefit any student who is trying to learn about rate of change and earn better grades. This resource can help students including those who:

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

Why it works:

  • Engaging Tutors: We make learning about rate of change 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

  • Understand the relationship between velocity and rate of change.
  • Describe how slopes and tangents relate to the rate of change.
  • Explain the Mean Value Theorem.
  • Explain how Rolle's Theorem relates to the Mean Value Theorem.
  • Define and graph derivatives.
  • Learn what it means to be differentiable.

7 Lessons in Chapter 6: Rate of Change: Tutoring Solution
Velocity and the Rate of Change

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.

Slopes and 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.

What is the Mean Value Theorem?

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.

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

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.

Derivatives: The Formal Definition

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.

Derivatives: Graphical Representations

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.

What It Means To Be 'Differentiable'

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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