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Ch 26: PLACE Mathematics: Rate of Change

About This Chapter

As you prepare for the PLACE Mathematics, it may be helpful for you to review material on slopes and rates of change. Use the lessons in this chapter to refresh your knowledge of slopes, rate of change, the mean value theorem and derivatives.

PLACE Mathematics: Rate of Change - Chapter Summary

As a future mathematics educator in the state of Colorado, you may need to take the PLACE Mathematics exam for certification. The lessons in this chapter will help you prepare for this exam as our instructors explain average and instantaneous rates of change, the mean value theorem and derivatives. After reviewing this chapter, you will have a better understanding of:

  • Slopes and rate of change
  • Differences between average and instantaneous rates of change
  • Mean value and Rolle's theorems
  • Definition and graphical representations of derivatives

When watching these lesson videos, be sure to ask our professional instructors any questions you may have. Also, complete the quizzes included in this chapter to reinforce the information presented and fortify any knowledge you don't have a firm grasp on using video tags that will take you to key points of the lesson videos.

PLACE Mathematics: Rate of Change Chapter Objectives

The PLACE Mathematics test is a paper-based certification exam composed of multiple-choice questions, and you'll have 4.5 hours to complete it. Of the questions on the PLACE Mathematics, 19% are part of the calculus and discrete mathematics section; this section is where you can find questions related to the topics in this chapter.

7 Lessons in Chapter 26: PLACE Mathematics: Rate of Change
Test your knowledge with a 30-question chapter practice test
Slopes and Rate of Change

1. 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.

Average and Instantaneous Rates of Change

2. Average and Instantaneous Rates of Change

When you drive to the store, you're probably not going the same speed the entire time. Speed is an example of a rate of change. In this lesson, you'll learn about the difference between instantaneous and average rate of change and how to calculate both.

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.

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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Other Chapters

Other chapters within the PLACE Mathematics: Practice & Study Guide course

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