Remember: The Extreme Value Theorem states that a continuous function on a closed interval always has an absolute minimum and maximum value. Below is the book definition.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi152oMlHri-ypqH-kvHailyXXbUTpI0RZMgkFPAde6eDEIdZ-KPNB32YVcO6HRUr961thyOpbEOFdGHM7ZyCQzAcXqvZhek91LR-DeCNAOfvQxmdbXZ-wUcw4cT8tzSGwzunkYWaOhgFQ/s320/Larson7_Ch03_Sect01_EVT.jpg)
Remember: A Critical Number is an x-value where the derivative is zero or does not exist. Maximum and minimum values may occur at these points, but not always. The book definition is below.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-oJVzHWX2jxNl-1XcaPlPFPrRlz7Pi544QizXcbvucuqdbeEWuG58wtBQAdpFMBeqMXN2j8ZdFsCbLC4je6Y6vUEUV-1tjYybC9VBC9h8UNEgiKrSTWQuhtkGBEYKwX9wkWGgJff9Kd4/s320/Larson7_Ch03_Sect01_CriticalNumbers.jpg)
Below are guidelines for finding Absolute Minima and Maxima.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhEcDBVd0PaG6WJeNkdwVkO_QCAgOAacAevLN4J_CCYFSmppo8kIiwpIZsYCP6IE_IQekR6Q6VLT-h2g79_ij2EArZC_7PeJFpuO4ccdghLDicMU1LUmQqZiQtdV6477I5NdrHXNOgeMFg/s320/Larson7_Ch03_Sect01_FindingGlobalExtrema.jpg)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhB1EGPPkls5vmoGbsthps0bAYfajxdG0l1jDNgJr5IYM12Zr7Ov-RMfHiXJgodwQB4G1S2sjtAzMhwXZSbhPc7hzIBoQi-35_gCe64MfBR5ByHIjkbbizZKlOJ0WTkyP1-mEXhlA-fzG0/s320/Larson7_Ch03_Sect01_Assignment01.jpg)
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