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

Sumi Vora

279Β resources
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## The Extreme Value Theorem

Not to be confused with the Mean Value Theorem is the Extreme Value Theorem: π₯

## Finding Absolute Extrema

There are two different places where an extreme value can occur: a critical point or an endpoint.Β π
Itβ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.Β
Once youβve found your relative extreme values on the domain, donβt forget to check your endpoints by plugging the ends of your domain into the function.Β βοΈ
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.Β π
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