Step 1:

(1)

The function is $\"\"$ .

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

$\"\"$ \ \

To find the relative extrema, by equating $\"\"$ .

$\"\"$

Consider $\"\"$ .

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

$\"\"$ .

$\"\"$ is positive for all values of $\"\"$ .

Therefore, the function has relative minimum at $\"\"$ .

$\"\"$ . \ \

Relative minima is $\"\"$ .

No relative maxima.

Step 1:

The function is $\"\"$ .

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

$\"\"$ \ \

To find the relative extrema by equating $\"\"$ to zero.

$\"\"$

$\"\"$ and $\"\"$ .

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

$\"\"$

The point is $\"\"$ .

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

$\"\"$

The point is $\"\"$ .

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

Step 2:

Using second derivative test, determine the relative extrema.

Consider $\"\"$ .

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

$\"\"$ .

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

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

\ \ Relative minima at $\"\"$ .

The relative minima at $\"\"$ .

Step 1:

The function is $\"\"$ .

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

$\"\"$ \ \

To find the relative extrema by equating $\"\"$ to zero.

$\"\"$

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

$\"\"$ .

The extrema point is $\"\"$ .

Using second derivative test, determine the relative extrema.

Consider $\"\"$ .

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

$\"\"$

Find the sign of $\"\"$ at $\"\"$ .

$\"\"$

Therefore, the function has relative maximum at $\"\"$ .

The relative maximum at $\"\"$ .

No relative minima.

The relative minima at $\"\"$ .

Solution:

The relative minimum at $\"\"$ .