Observe the graph :

The function has relative maxima at .

The funcction has relative minima at . It is also appears that  and , so the conjecture that this function has no absolute extrema.

Support numerically :

Construct the table of values.

Choose -values on either side of the estimated -value for each extremum, as well as one very large and one very small value for .

 Observe the above table :

Because and , there is a relative maximum in the interval .The approximate value of this relative maximum is .

 Because and , there is a relative minimum in the interval .The approximate value of this relative minimum is .

and , which supports the conjecture that the function has no absolute extrema.

The relative maximum is at .

The relative minimum is at .