$\"\"$

The function is $\"\"$ .

Find the $\"\"$ -intercept by substitute $\"\"$ in the above function.

$\"\"$

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

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

$\"\"$

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

$\"\"$

Find the extrema for $\"\"$ .

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

$\"\"$ .

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

$\"\"$

$\"\"$ .

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

Equate the numerator equal to zero.

$\"\"$

The critical point is at $\"\"$ .

$\"\"$

Find the points of inflection.

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

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

$\"\"$

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

$\"\"$

The function does not have inflection points.

$\"\"$

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
$\"\"$	\ $\"\"$ \	Relative maximum

Relative maximum 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 are $\"\"$ , $\"\"$ and $\"\"$ .

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

Relative maximum point is $\"\"$ .

The function has no horizontal asymptote and vertical asymptote.

$\"\"$

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

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

Relative maximum point is $\"\"$ .