Graphs of Functions & Their Derivatives

Sarah Miller
7 min read
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Study Guide Overview
This study guide covers local and global extrema, focusing on the identification and classification of critical points. It explains the different types of critical points: local minimums and maximums, points of inflection, and points where the derivative is undefined. Examples of finding critical points for polynomial and root functions are provided, along with practice questions and exam strategies.
#Study Notes: Local Extrema versus Global Extrema
#Table of Contents
- Introduction
- Local Extrema vs. Global Extrema
- Critical Points
- Practice Questions
- Glossary
- Summary and Key Takeaways
- Exam Strategy
#Introduction
In calculus, understanding the concepts of local and global extrema and critical points is essential for analyzing and interpreting the behavior of functions. This guide will help you distinguish between these concepts, identify critical points, and apply this knowledge effectively in exams.
#Local Extrema vs. Global Extrema
#Definitions
- Extrema: Refers to the maximum and minimum points on the graph of a function.
- Global (Absolute) Extrema: The highest (maximum) or lowest (minimum) value of the function over its entire domain.
- Local (Relative) Extrema: The highest or lowest value of the function within a specific interval of the domain.
Global extrema are the absolute highest or lowest points of a function over its entire domain, while local extrema are the highest or lowest points within a specific interval.
Remember that every global...

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