The first derivative test is performed by checking the first derivative right before the point being checked and right after. If the derivative switches from positive to negative there is a local maximum there, alternatively if the derivative switches from negative to positive there is a local minimum there. If the sign of the derivative stays the same there is no extrema at that point.

Example

Given the function find the local minimum(s) and local maximum(s) over the interval

is shown in blue, with critical points shown as red dots. Additionally the derivative of is also shown in green.


				0
	Decreasing	Minimum	Increasing	Maximum	Decreasing

Note

Tables like the example above are a good way of finding all the local extrema on an interval.

There are 2 local extrema, 1 local minimum at and 1 local maximum at .