Ch 14: Rate of Change in Precalculus: Tutoring Solution

About This Chapter

The Rate of Change chapter of this High School Precalculus 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 information involving rate of change required in a typical high school precalculus course.

How it works:

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

  • Struggle with understanding velocity and rate of change, slopes and rate of change, derivatives or any other rate of change 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 unit
  • Cope with ADD or ADHD
  • Want to get ahead in precalculus
  • Don't have access to their math teacher outside of class

Why it works:

  • Engaging Tutors: We make learning 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 precalculus tutor, these video lessons are thoroughly reviewed.
  • Convenient: Imagine a tutor as portable as your laptop, tablet or smartphone. Learn 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

  • Find out how to use motion to define the rate of change.
  • Learn to relate slopes and tangents to motion and rate of change.
  • Describe the Mean Value Theorem and represent it graphically.
  • Show how Rolle's Theorem is related to the Mean Value Theorem.
  • Understand the derivative and graph it.
  • Describe what it means to be differentiable.

7 Lessons in Chapter 14: Rate of Change in Precalculus: Tutoring Solution
Test your knowledge with a 30-question chapter practice test
Velocity and the Rate of Change

1. Velocity and the Rate of Change

The rate of change refers to how one variable changes based on another variable. Learn about velocity and rate of change by reading an example of the velocity of my drive to work. Then, learn about velocity and inconstant slopes.

Slopes and Rate of Change

2. Slopes and Rate of Change

The rate of change is shown through one variable as it changes the function of another variable and can be seen furthermore as location changes as a function of time. Learn more about slopes, rates of change, and the rate of velocity.

What is the Mean Value Theorem?

3. What is the Mean Value Theorem?

In physics, the Mean Value Theorem is an important aspect of working with rates of change. In this lesson, take a look at the average rate of change of three drivers and review instantaneous rate of change to better understand the Mean Value Theorem.

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

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

Rolle's theorem is based on the ideas of the mean value theorem, where objects in motion eventually travel at their average velocity speed. Learn the concept behind Rolle's theorem through how it appears in both equations, and graphs.

Derivatives: The Formal Definition

5. Derivatives: The Formal Definition

The derivative in calculus is the rate of change of a function. In this lesson, explore this definition in greater depth and learn how to write derivatives.

Derivatives: Graphical Representations

6. Derivatives: Graphical Representations

The derivative of a point can be found using the graph of a function. Learn how to find the tangent of a curve at a point from a graphical representation of a function.

What It Means To Be 'Differentiable'

7. What It Means To Be 'Differentiable'

Functions with smooth graphs that allow us to calculate derivatives are considered differentiable. Learn more about the definition of 'differentiable' through examples.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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More Exams
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Other Chapters

Other chapters within the High School Precalculus: Tutoring Solution course