$\"\"$

The function is $\"\"$ .

Find the $\"\"$ -intercept by substitute $\"\"$ .

$\"\"$

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

The $\"\"$ -intercepts are $\"\"$ and $\"\"$ .

Find the $\"\"$ -intercept by substitute $\"\"$ .

$\"\"$

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

$\"\"$

Find the extrema for $\"\"$ .

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

$\"\"$ .

Power rule differenciation : $\"\"$ .

$\"\"$

$\"\"$ .

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

$\"\"$

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

The critical numbers are $\"\"$ and $\"\"$ .

$\"\"$

Find the inflection points of the graph $\"\"$ .

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

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

$\"\"$ .

Power rule of derivatives : $\"\"$ .

$\"\"$ .

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

To find the inflection point, equate $\"\"$ to zero.

$\"\"$ .

$\"\"$

The possible inflection point occurs at $\"\"$ .

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

$\"\"$

The inflection point of the graph $\"\"$ is $\"\"$ .

$\"\"$

The critical numbers are $\"\"$ and $\"\"$ .

Relative extrema points exist at critical numbers.

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

$\"\"$

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

$\"\"$

$\"\"$ .

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

\ \

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

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

Relative maximum point is $\"\"$ .

Relative minimum point is $\"\"$ .

$\"\"$

Find asymptote of function $\"\"$ .

To find horizontal asymptote $\"\"$ .

$\"\"$ .

The function has no horizontal asymptote.

Since the function has no denominator the function is true for all real values.

Thus, the function has no vertical asymptote.

$\"\"$

Graph the function $\"\"$ .

$\"\"$

The $\"\"$ -intercepts are $\"\"$ and $\"\"$ .

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

Relative maximum point is $\"\"$

Relative minimum point is $\"\"$ .

The inflection point of the graph $\"\"$ is $\"\"$ .

Graph the function $\"\"$ .

$\"\"$ .