The closed interval method finds the global maximum and global minimum of a continuous
function 
on a closed interval ![[a,b]](/images/equations/ClosedIntervalMethod/Inline2.svg)
. The extreme
value theorem guarantees that both values are attained.
Evaluate 
at the endpoints 
and 
and at every interior critical
point, where 
or the derivative does not exist. An interior extremum
must be a critical point. The largest and smallest
of the resulting values are therefore the global maximum
and global minimum.
For example, 
on ![[0,2]](/images/equations/ClosedIntervalMethod/Inline8.svg)
has a single interior critical point at 
. The values at 0, 1, and 2 are 0, 
, and 2, so the global
minimum is 
at 
and the global maximum is 2 at 
.
