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Ch 25: MTLE Mathematics: Rate of Change & Derivatives

About This Chapter

This chapter on Rate of Change and Derivatives is just the ticket for an effective and painless review of the sort of subject-relevant material you'll encounter on the MTLE Mathematics exam.

MTLE Mathematics: Rate of Change and Derivatives - Chapter Summary

The lessons in this chapter exhibit the various applications of derivatives and the rate of change in mathematical procedures, paying particular attention to the kind of topics on this subject that you'll be seeing on the MTLE Mathematics exam, including:

  • Velocity, slopes and the rate of change
  • Finding instantaneous rate of change of a function
  • The mean value theorem
  • Rolle's Theorem
  • Defining and graphically representing derivatives
  • Defining 'differentiable'

Verifying your comprehension of these topics will be a simple task with practice quizzes at the end of each lesson that you can take as many times as you want. In the video lessons, these helpful quizzes provide you with the option to hop back to the question-relevant point of the lesson should you answer incorrectly. All the lesson quizzes are available for printing as worksheets if you'd like to use them for offline study.

8 Lessons in Chapter 25: MTLE Mathematics: Rate of Change & Derivatives
Test your knowledge with a 30-question chapter practice test
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.

Finding Instantaneous Rate of Change of a Function: Formula & Examples

3. Finding Instantaneous Rate of Change of a Function: Formula & Examples

In this lesson, you will learn about the instantaneous rate of change of a function, or derivative, and how to find one using the concept of limits from Calculus.

What is the Mean Value Theorem?

4. 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

5. 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

6. 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

7. 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'

8. 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 MTLE Mathematics: Practice & Study Guide course

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