$\"\"$

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

Find the intercepts :

To find the $\"\"$ - intercept, substitute $\"\"$ in the function.

$\"\"$

Solve $\"\"$ in the interval $\"\"$ .

$\"\"$

$\"\"$ doesnot exist for real values of $\"\"$ .

The solutions of $\"\"$ to $\"\"$ in the interval $\"\"$ .

Therefore, the $\"\"$ - intercepts are $\"\"$ to $\"\"$ .

To find the $\"\"$ -intercept, substitute $\"\"$ in the function.

$\"\"$

$\"\"$

The $\"\"$ - intercept is $\"\"$ .

$\"\"$

Find the relative extrema for the function $\"\"$

Consider $\"\"$ .

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

$\"\"$ .

$\"\"$

$\"\"$ .

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

$\"\"$ .

$\"\"$

$\"\"$ .

There is no solution for $\"\"$ in the interval $\"\"$ .

Thus, the critical points occur at $\"\"$ to $\"\"$ .

If $\"\"$ , then $\"\"$ .

If $\"\"$ , then $\"\"$ .

The relative maximum is $\"\"$ .

The relative minimum is $\"\"$ .

$\"\"$

Find the points of inflection

Consider $\"\"$ .

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 ,

The relative maximum is $\"\"$ .

The relative minimum is $\"\"$ .

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

There is no horizontal and vertical asymptote.

$\"\"$

The relative maximum is $\"\"$ .

The relative minimum is $\"\"$ .

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

There is no horizontal and vertical asymptote.

Graph the function $\"\"$ .

$\"\"$