Use the input box for f(x) to define the function.

Extreme values (maximum/minimum values) can be classified as [b]local [/b]or [b]global[/b]. [br][list][*]A maximum/minimum is [b]local [/b]if it is only the largest/smallest value of f in a small viewing window around it. In other words, if you move far enough away from a local maximum/minimum you can find other values of the function that are larger/smaller. [/*][*]A maximum/minimum is [b]global [/b]if it is the largest/smallest value across the entire domain of f. In other words, a global maximum is the largest local maximum value and a global minimum is the smallest local minimum value. [/*][/list][br]The [b]Extreme Value Theorem [/b]states that a function defined on a closed interval [a,b] is guaranteed to have both a global maximum and a global minimum. To find global extreme values:[br][list][*]Find all the critical points of f between the endpoints of the domain, a and b. [/*][*]Evaluate f(x) at the critical points and endpoints. These are the only locations where f can have maximum or minimum values. [/*][*]Because a global maximum/minimum is guaranteed to exist (by the theorem), the largest f(x) value gives the global maximum and the smallest f(x) value gives the global minimum. [/*][/list]