$\"\"$

\

The function is $\"\"$ , $\"\"$ .

\

Apply first derivative with respect to $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Find the relative extrema , by equating $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ or $\"\"$

\

$\"\"$

\

Solve for $\"\"$

\

The general solution of sine function $\"\"$ is $\"\"$ .

\

Where $\"\"$

\

Then the values of $\"\"$ are $\"\"$ , $\"\"$ , $\"\"$ .....

\

Solve for $\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

The general solution of sine function $\"\"$ is $\"\"$ .

\

Where $\"\"$

\

The values of $\"\"$ are $\"\"$ , $\"\"$ , $\"\"$ ....

\

So the critical values of $\"\"$ are $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .

\

$\"\"$

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

The relative extrema points are $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .

\

$\"\"$

\

Using the second derivative test.

\

Apply second derivative with respect to $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

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

Point	$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	\ $\"\"$ \	$\"\"$	$\"\"$	$\"\"$
Sign of $\"\"$	\ $\"\"$ \	\ $\"\"$ \	$\"\"$	$\"\"$
\ Conclusion \	\ Relative maximum \	Relative maximum	\ Relative minimum \	\ Relative minimum \

\

$\"\"$

\

The relative maximum at $\"\"$ and $\"\"$ .

\

The relative minimum at $\"\"$ and $\"\"$ .