The function is .

All possible values of , is domain of the function.

The domain of is .

Intercept:

To find the -intercept,substitute in the function.

.

Apply zero product property.

and

and

and

and

The -intercepts are and .

To find the -intercept, substitute in the function.

The -intercept is .

Find the extrema.

The function is .

Apply derivative on each side with respect to .

Apply product rule of derivatives: .

In this case and .

.

Find the critical numbers by equating .

The critical numbers are .

The domain of is .

Relative extrema points exist at critical numbers, Then intervals are ,  and .

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

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

The function has relative maximum and minimum at critical number .

Substitute in .

.

Substitute in .

.

The relative maximum is .

The relative minimum is .

Inflection points:

.

Again apply derivative on each side with respect to .

Apply quotient rule of derivatives: .

.

Find inflection points by equating .

and

and

and .

is not in the domain.

The possible inflection points occurs at .

Substitute in .

.

The inflection point is .

Consider the test intervals as .

\ Interval \	Test Value	Sign of	Concavity
		\ \	\ Up \
		\ \	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 .

.