Graphing Rational Functions. Example (1) For the following function: determine the intervals of increase/decrease, the intervals of upward/downward concavity,

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Graphing Rational Functions

Example (1) For the following function: determine the intervals of increase/decrease, the intervals of upward/downward concavity, the points of extremum and inflection, the intersections with the axes and the asymptotes and then graph it.

Asymptotes

Intersection with the Axes & Extremum See Appendix

Intervals of increase/decrease

Another Way to show extremum First Derivative Test

Concavity

Graph

Example (2) For the following function: determine the intervals of increase/decrease, the intervals of upward/downward concavity, the points of extremum and inflection, the intersections with the axes and the asymptotes and then graph it.

Asymptotes

Intersection with the Axes & Extremum See Appendix

Intervals of increase/decrease

Another Way to show extremum First Derivative Test

Concavity

Graph

Example (3) For the following function: determine the intervals of increase/decrease, the intervals of upward/downward concavity, the points of extremum and inflection, the intersections with the axes and the asymptotes and then graph it.

Asymptotes

Intersection with the Axes & Extremum See Appendix

Intervals of increase/decrease

Another Way to show extremum First Derivative Test

Concavity

Graph

Appendix Differentiating & Simplifying

Example(1)

Example(2)

Example(3)

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