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

1 min readβ€’march 31, 2020

Sumi Vora

Sumi Vora


AP Calculus AB/BC ♾️

279Β resources
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The Extreme Value Theorem

Not to be confused with the Mean Value Theorem is the Extreme Value Theorem: πŸ’₯
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Finding Absolute Extrema

There are two different places where an extreme value can occur: a critical point or an endpoint.Β πŸ˜‰
It’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 you’ve found your relative extreme values on the domain, don’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. 🌎
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