# Ch 26: NES Math: Rate of Change

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### About This Chapter

## NES Math: Rate of Change - Chapter Summary

This chapter's lessons offer a review of rates of change, derivatives and mean value theorem and can help you answer these types of questions on the NES Math test. Use our videos and quizzes to refresh your knowledge of topics such as:

- Rate of change and slopes
- Average and instantaneous rates of change
- Mean value theorem, including Rolle's theorem
- Derivatives and how they are graphically represented
- The definition of differentiable

Our instructors understand what success on the NES Math test requires and use snappy narration, animations and examples from the real world to make your review informative and fun. You may contact the instructors through our ask-an-expert message board if you have questions. You can test your knowledge through self-assessment quizzes at the end of each lesson, and a clickable Timeline accompanies each video and makes it easy to jump to key points in the lesson for review.

### NES Math: Rate of Change - Chapter Objectives

In Arizona, New Mexico, Oregon, Washington and Wisconsin, passing the NES Math test is one of the requirements for certification to teach mathematics at the secondary level. The test is computer-based and consists entirely of multiple-choice questions. You can get good practice with these types of questions through our lesson quizzes and the chapter exam at the end of all the lessons on functions. These tests also let you assess your study and see where you need additional review.

The NES Math test is divided into five content domains. Questions on the material reviewed in this Rate of Change chapter are in the Mathematical Processes and Number Sense content domain, which accounts for 19% of the test's total score.

### 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.

### 2. Average and Instantaneous Rates of Change

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

### 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.

### 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.

### 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.

### 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.

### 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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### Other Chapters

Other chapters within the NES Mathematics (304): Practice & Study Guide course

- NES Math: Properties of Real Numbers
- NES Math: Fractions
- NES Math: Decimals & Percents
- NES Math: Ratios & Proportions
- NES Math: Units of Measure & Conversions
- NES Math: Logic
- NES Math: Reasoning
- NES Math: Vector Operations
- NES Math: Matrix Operations & Determinants
- NES Math: Exponents & Exponential Expressions
- NES Math: Algebraic Expressions
- NES Math: Linear Equations
- NES Math: Inequalities
- NES Math: Absolute Value
- NES Math: Quadratic Equations
- NES Math: Polynomials
- NES Math: Rational Expressions
- NES Math: Radical Expressions
- NES Math: Systems of Equations
- NES Math: Complex Numbers
- NES Math: Functions
- NES Math: Piecewise Functions
- NES Math: Exponential & Logarithmic Functions
- NES Math: Continuity of Functions
- NES Math: Limits
- NES Math: Derivative Rules
- NES Math: Graphing Derivatives
- NES Math: Applications of Derivatives
- NES Math: Area Under the Curve & Integrals
- NES Math: Integration Techniques
- NES Math: Applications of Integration
- NES Math: Foundations of Geometry
- NES Math: Geometric Figures
- NES Math: Properties of Triangles
- NES Math: Triangle Theorems & Proofs
- NES Math: Parallel Lines & Polygons
- NES Math: Quadrilaterals
- NES Math: Circles & Arc of a Circle
- NES Math: Conic Sections
- NES Math: Geometric Solids
- NES Math: Analytical Geometry
- NES Math: Trigonometric Functions
- NES Math: Trigonometric Graphs
- NES Math: Solving Trigonometric Equations
- NES Math: Trigonometric Identities
- NES Math: Sequences & Series
- NES Math: Graph Theory
- NES Math: Set Theory
- NES Math: Statistics Overview
- NES Math: Summarizing Data
- NES Math: Tables, Plots & Graphs
- NES Math: Probability
- NES Math: Discrete Probability Distributions
- NES Math: Continuous Probability Distributions
- NES Math: Sampling
- NES Math: Regression & Correlation