Extreme Value Theorem, Global vs Local Extrema, and Critical Points
Study Guide Overview
This study guide covers the Extreme Value Theorem, differentiating between global and local extrema, and identifying critical points. It explains how to apply the Extreme Value Theorem to continuous functions on closed intervals. The guide also discusses finding critical points by checking where the derivative is zero or undefined. Practice problems involving identifying critical points and extrema from graphs, and applying the Extreme Value Theorem are included.
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Question 1 of 11
A continuous function is defined on the closed interval . According to the Extreme Value Theorem, what is guaranteed?
The function has at least one critical point
The function has both a global maximum and a global minimum within the interval
The function is differentiable on the interval
The function has a local maximum at every critical point