$\"\"$

The function is $\"\"$ .

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

$\"\"$

Inverse trigonometric functions of Derivative: $\"\"$ .

$\"\"$

Again apply derivative on each side with respect to $\"\"$ .

$\"\"$

$\"\"$

(a)

To find the relative extrema, take $\"\"$ .

$\"\"$

Equate denominator to zero.

$\"\"$

Substitute $\"\"$ in the function $\"\"$ .

$\"\"$

Relative extrema is $\"\"$ .

Substitute $\"\"$ in the function $\"\"$ .

$\"\"$

Relative extrema is $\"\"$ .

Relative extrema are $\"\"$ and $\"\"$ .

Identify the nature of the extrema points.

\ \

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

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

$\"\"$

(b)

To find the inflection points, take $\"\"$ .

$\"\"$

Substitute $\"\"$ in the function $\"\"$ .

$\"\"$

The inflection point is $\"\"$ .

$\"\"$

(c)

To find the Horizontal asymptotes, consider $\"\"$ .

$\"\"$

No horizontalasymptote.

Substitute $\"\"$ in the function of $\"\"$

$\"\"$

No vertical asymptotes.

There are no asymptotes.

$\"\"$

Graph:

The function is $\"\"$ .

$\"\"$

Observe the graph,

Relative extrema are $\"\"$ and $\"\"$ .

The inflection point is $\"\"$ .

There are no asymptotes.

$\"\"$

Relative extrema are $\"\"$ and $\"\"$ .

The inflection point is $\"\"$ .

There are no asymptotes.