$\"\"$

The function is $\"\"$ and interval is $\"\"$ .

Find the intercepts :

Find the $\"\"$ -intercept, substitute $\"\"$ in the function.

$\"\"$

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

Find the $\"\"$ -intercept, substitute $\"\"$ in the function.

$\"\"$

The function does not have $\"\"$ - intercept.

$\"\"$

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

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

$\"\"$

Find the critical number, substitute $\"\"$ .

$\"\"$

The solutions of $\"\"$ are $\"\"$ and $\"\"$ in the interval $\"\"$ . $\"\"$

Find the points of inflection :

Consider $\"\"$ .

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

$\"\"$

Find inflection points, equate $\"\"$ to zero.

$\"\"$

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

$\"\"$ is not defined.

$\"\"$ when $\"\"$ .

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

$\"\"$

The critical numbers is $\"\"$ 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 $\"\"$ .

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 :

Graph the function is $\"\"$ .

$\"\"$

Observe the graph :

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

Relative maximum point is $\"\"$ .

Relative minimum point is $\"\"$ .

The function has no horizontal asymptote and vertical asymptote.

$\"\"$

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

Relative maximum point is $\"\"$ .

Relative minimum point is $\"\"$ .

The function has no horizontal asymptote and vertical asymptote.