Observe the graph :

The function has relative maxima at  and .

The funcction has relative minima at and . 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 table :

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

The relative minima are at .