The function is .

Intercept :

To find the -intercept substitute in the function.

, , and .

Imaginary roots are not considered.

Hence -intercepts are , and .

To find the -intercept substitute in the function.

The -intercept is .

Find the extrema for  .

Differentiate on each side  with respect to .

.

To find the critical numbers we make .

.

, , and  .

Imaginary roots are not considered.

Hence critical numbers are and .

Find the points of inflection.

The first derivative of is .

Differentiate on each side with respect to .

.

.

The second derivative of is .

Equate to .

.

.

The inflection points occurs at .

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 minimum
	\ \	Relative maximum

Relative maximum point is

Relative minimum point is .

Find asymptote of function .

To find horizontal asymptote .

.

.

There is no horizontal asymptote

To find vertical asymptote, denominator of the functionis equates to zero.

The function is defined for all values of .

There is no vertical asymptote.

Graph:

Graph the function .

Observe the graph ,

The intercepts are , , and .

Relative maximum point is .

Relative minimum point is . 

The  inflection points occurs at  .

There is no horizontal asymptote.

There is no vertical asymptote.

Graph the function .