Graphs of Functions & Their Derivatives
Sarah Miller
5 min read
Study Guide Overview
This study guide covers the Candidates Test for finding global extrema of continuous functions on closed intervals. It explains the Extreme Value Theorem, critical points, and endpoints. The guide outlines the steps for applying the test, including checking for continuity, finding critical points, and evaluating the function at critical points and endpoints. It also provides a worked example, practice questions, and a glossary of key terms.
#Candidates Test for Global Extrema
#Table of Contents
- Introduction
- Key Concepts
- Steps for the Candidates Test
- Exam Tip
- Worked Example
- Practice Questions
- Glossary
- Conclusion and Key Takeaways
#Introduction
The candidates test is a method used to determine the global extrema (maximum and minimum) of a continuous function on a closed interval. This is based on the extreme value theorem, which guarantees the existence of at least one global maximum and one global minimum for continuous functions on closed intervals.
#Key Concepts
- Extreme Value Theorem: Guarantees that a continuous function on a closed interval has at least one global maximum and one global minimum.
- Global Extrema: The largest and smallest values of a function within a given interval.
- Critical Points: Points within the interval where the first derivative of the function is zero or undefined.
- Endpoints: The values of the function at the boundaries of the interval. </key_conce...
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