The function is .

The domain of a function is all possible values of .

The domain of the function is .

Intercept:

To find the -intercept, substitute in the function.

Apply zero product property.

and

and

and .

The -intercepts are and .

To find the -intercept, substitute in the function.

The -intercept are and .

Find the extrema.

The function is .

Apply derivative on each side  with respect to .

.

Apply product rule of derivatives: .

In this case and .

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To find the critical numbers by equating .

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The critical number is .

The domain of is .

Relative extrema points exist at critical numbers.

The test  intervals are and .

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

Test itervals	Test value	Sign of	Conclusion
		\ \	Increasing
		\ \	Decreasing

The function has relative maximum at .

Substitute in .

.

The relative maximum at .

Inflection points:

.

Again apply derivative on each side with respect to .

.

Apply quotient rule of derivatives: .

.

Find inflection points by equating we make.

.

.

is not in the domain.

Therefore, there is no inflection points.

Consider the test intervals as .

\ Interval \	Test Value	Sign of	Concavity
		\ \	\ Down \

Asymptotes :

Vertical asymptote:

Vertical asymptote exist when denominator is zero.

Equate denominator to zero.

The function is .

There is no vertical asymptote.

Horizontal asymptote:

The line is called a horizontal asymptote of the curve if either

  or

.

.

There is no horizontal asymptote.

Graph:

Graph the function .

Graph:

Graph the function .

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