$\"\"$

The function is $\"\"$ and intervals are $\"\"$ .

Find the extrema :

The function is $\"\"$ .

Differentiate on each side with respect to $\"\"$ .

$\"\"$ .

$\"\"$

$\"\"$ .

To find the critical numbers, equate $\"\"$ to $\"\"$ .

$\"\"$ .

$\"\"$

$\"\"$ .

The critical number is $\"\"$ .

$\"\"$

Find the points of inflection.

The first derivative of $\"\"$ is $\"\"$ .

Differentiate on each side with respect to $\"\"$ .

$\"\"$ .

Apply $\"\"$ .

$\"\"$

The second derivative of $\"\"$ is $\"\"$ .

Equate $\"\"$ to $\"\"$ .

$\"\"$ .

$\"\"$

The inflection points occurs at $\"\"$ .

Substitute $\"\"$ in the function.

$\"\"$

$\"\"$ .

The inflection points occurs at $\"\"$ and $\"\"$ .

$\"\"$

Relative extrema points exist at critical numbers, Then intervals are $\"\"$ and $\"\"$ .

$\"\"$

Perform first derivative test to identify the nature of the extrema.

\ \

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

Test itervals	Test value	Sign of $\"\"$	Conclusion
$\"\"$	$\"\"$	\ $\"\"$ \	Relative minimum
$\"\"$	$\"\"$	\ $\"\"$ \	Relative minimum

No relative extrema point.

$\"\"$

Find asymptote of function $\"\"$ .

To find horizontal asymptote $\"\"$ .

$\"\"$

$\"\"$ .

There is no horizontal asymptote.

To find vertical asymptote,denominator of the function is equated to zero.

The function is defined for all values of $\"\"$ .

There is no vertical asymptote.

$\"\"$

Graph :

Graph the function $\"\"$ .

$\"\"$

Observe the graph ,

No relative extrema point.

The inflection points occurs at $\"\"$ and $\"\"$ .

There is no horizontal and vertical asymptote.

$\"\"$

No relative extrema point.

The inflection points occurs at $\"\"$ and $\"\"$ .

There is no horizontal and vertical asymptote.

Graph the function $\"\"$ .

Graph:

$\"\"$