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Unit 5

5.2 Extreme Value Theorem, Global vs Local Extrema, and Critical Points

1 min readโ€ขmarch 31, 2020

Sumi Vora


The Extreme Value Theorem

Not to be confused with the Mean Value Theorem is the Extreme Value Theorem: ๐Ÿ’ฅ

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Finding Absolute Extrema

There are two different places where an extreme value can occur: a critical point or an endpoint.ย ๐Ÿ˜‰

Itโ€™s possible that a local extreme value can be the absolute maximum or minimum, so you need to find all of the relative maximum and minimum values within the domain.ย 

Once youโ€™ve found your relative extreme values on the domain, donโ€™t forget to check your endpoints by plugging the ends of your domain into the function.ย โ˜‘๏ธ

Now that you have a set of values (both relative extrema and endpoint values), compare them to pick the biggest and smallest value. This gives you your absolute extreme values.ย ๐ŸŒŽ

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