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Definition of Differentiation

Sarah Miller

Sarah Miller

4 min read

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Study Guide Overview

This study guide covers the average rate of change, including its definition, formula (Δy/Δx), and representation using function notation. It provides a worked example and practice questions to reinforce understanding. Key terms like slope are defined in a glossary, and the guide emphasizes the importance of the average rate of change in calculus.

Average Rate of Change

Table of Contents

  1. Introduction
  2. Definition and Formula
  3. Function Notation
  4. Worked Example
  5. Practice Questions
  6. Glossary
  7. Summary and Key Takeaways

Introduction

Understanding the average rate of change is crucial in analyzing how quantities change over intervals. This concept is foundational in calculus and provides insight into the behavior of functions.

Definition and Formula

What is the Average Rate of Change?

Average Rate of Change is the slope of the line segment connecting two points on a graph. It is calculated as:

Average Rate of Change=ΔyΔx=y2−y1x2−x1\text{Average Rate of Change} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}

Where $ \left( x_1, y_1 \right)...

Previous Topic - Intermediate Value TheoremNext Topic - Instantaneous Rate of Change

Question 1 of 6

Ready to calculate? 🚀 What is the average rate of change of a function between the points (1, 4) and (3, 10)?

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