$\"\"$

The function is $\"\"$ .

Intercept :

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

$\"\"$ .

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

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

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

$\"\"$

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

$\"\"$

Find the extrema for $\"\"$ .

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

$\"\"$ .

$\"\"$

Find the critical numbers by equating $\"\"$ to $\"\"$ .

$\"\"$ .

$\"\"$

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

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

$\"\"$

Find the points of inflection.

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

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

$\"\"$

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

$\"\"$ .

$\"\"$

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

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

$\"\"$

The critical numbers is $\"\"$ .

Relative extrema points exist at critical numbers.

Substitute $\"\"$ in the function.

$\"\"$

$\"\"$ .

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

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

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

Relative minimum point is $\"\"$

$\"\"$

Find asymptote of function $\"\"$ .

To find horizontal asymptote $\"\"$ .

$\"\"$ .

$\"\"$

$\"\"$ .

There is no horizontal asymptote

To find vertical asymptote,equate numarator to zero.

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

There is no vertical asymptote.

$\"\"$

Graph the function $\"\"$ .

$\"\"$

Observe the graph ,

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

Relative maximum point is $\"\"$ .

There is no inflection points occurs.

There is no horizantal and vertical asymptote.

$\"\"$

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

Relative maximum point is $\"\"$ .

There is no inflection points occurs.

There is no horizantal and vertical asymptote.

Graph the function $\"\"$ .

$\"\"$