Observe the graph :

The function $\"\"$ has absolute maximum at $\"\"$ , a relative minimum at $\"\"$ .

The funcction $\"\"$ absolute maximum 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 an absolute maximum in the interval $\"\"$ .The approximate value of the absolute maximum is $\"\"$ .Likewise, because $\"\"$ and $\"\"$ , there is a absolute maximum in the interval $\"\"$ .The approximate value of absolute maximum is $\"\"$ .