Not to be confused with the Mean Value Theorem is the Extreme Value Theorem: 💥
There are two different places where an extreme value can occur: a critical point or an endpoint. 😉
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.
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. ☑️
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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5.2Extreme Value Theorem, Global vs Local Extrema, and Critical Points