$\"\"$

The function is $\"\"$ .

Graph:

Graph the function is $\"\"$ .

Apply derivative on each side with respect to $\"\"$ .

$\"\"$

Find the critical numbers of $\"\"$ on the interval $\"\"$ by equating $\"\"$ to zero.

$\"\"$

$\"\"$ , where $\"\"$ is an integrer.

Consider $\"\"$ .

Therefore, $\"\"$ .

Test intervals are $\"\"$ , $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Interval	test value	Sign of $\"\"$	Conclusion
$\"\"$	$\"\"$	$\"\"$	Increasing
$\"\"$	$\"\"$	$\"\"$	Decreasing
$\"\"$	$\"\"$	$\"\"$	Increasing
$\"\"$	$\"\"$	$\"\"$	Decreasing
$\"\"$	$\"\"$	$\"\"$	Increasing
$\"\"$	$\"\"$	$\"\"$	Decreasing

Observe the pattern of conclusion in the table,

For every odd multiples of pi to even multiples of pi the function is increasing and for even multiples of pi to odd multiples of pi the function is decreasing.

Therefore function has local minimum at every even multiples of pi and it has local minimum at every odd multiples of pi.