Ch 7: Rate of Change

Watch video lessons on rate of change to learn about the mean value theorem, Rolle's theorem, derivatives and more. Each lesson is accompanied by a short multiple-choice quiz you can use to check your understanding of these math topics.

Motion relates to the rate of change, which is how fast a position changes over time, or in more of a mathematical sense, how fast one variable changes as a function of another variable. To better understand how this works, check out our lessons on the rate of change. This particular chapter will help you learn about the following:

• How motion is related to slopes and tangents
• The mean value theorem
• Rolle's Theorem
• Derivatives, the definitive elements of calculus
• Derivative graphing

Video Objectives
Velocity and the Rate of Change Discover how to use motion to define the rate of change. See how fast one variable changes as a function of another variable.
Slopes and Rate of Change Learn how slopes and tangents relate to motion and rate of change.
What Is the Mean Value Theorem? Get an explanation of the Mean Value Theorem and learn to demonstrate it graphically.
Rolle's Theorem: A Special Case of the Mean Value Theorem Explore Rolle's Theorem in terms of the Mean Value Theorem. See Rolle's Theorem as a graph and as an equation.
Derivatives: The Formal Definition Learn to formally define the derivative and discover how the derivative is related to the instantaneous rate of change.
Derivatives: Graphical Representations Take a graphical look at the definitive element of calculus: the derivative.
What It Means To Be 'Differentiable' Define what it means to be differentiable.

7 Lessons in Chapter 7: Rate of Change
Test your knowledge with a 30-question chapter practice test
Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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