Observe the graph :

The function has absolute maximum at .

The function has a relative maximum at and relative minimum at .

It is also appears that  and , so the conjecture that this function has no absolute minimum.

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 an absolute maximum in the interval . The approximate value of the absolute maximum is . Like wise, because and , there is a relative minimum in the interval . The approximate value of this relative minimum is .

Because and , there is a relative maximum in the interval .

The approximate value of this relative maximum is .

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

The absolute maximum is at .

The relative maximum is and relative minimum is at .