# The Extreme Value Theorem The extreme value theorem dictates that **every [[Function Discontinuities|continuous]] function on a closed interval has an absolute maximum and an absolute minimum**. The **candidates** for those values are the **edges of the domain**, and **all values where the function’s first [[Derivative]] is 0**. Extreme value is here defined as an $x_e$ such that we cannot find another $x$ for which $f(x) > f(x_e)$. If trying to find a minimum or a maximum specifically (and not extreme values in general), you can use [[The Second Derivative Test]].