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Graphing Rational Functions. Example (1) For the following function: determine the intervals of...

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  • Slide 1
  • Graphing Rational Functions
  • Slide 2
  • 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.
  • Slide 3
  • Asymptotes
  • Slide 4
  • Intersection with the Axes & Extremum See Appendix
  • Slide 5
  • Intervals of increase/decrease
  • Slide 6
  • Another Way to show extremum First Derivative Test
  • Slide 7
  • Concavity
  • Slide 8
  • Graph
  • Slide 9
  • 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.
  • Slide 10
  • Asymptotes
  • Slide 11
  • Intersection with the Axes & Extremum See Appendix
  • Slide 12
  • Intervals of increase/decrease
  • Slide 13
  • Another Way to show extremum First Derivative Test
  • Slide 14
  • Concavity
  • Slide 15
  • Graph
  • Slide 16
  • 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.
  • Slide 17
  • Asymptotes
  • Slide 18
  • Intersection with the Axes & Extremum See Appendix
  • Slide 19
  • Intervals of increase/decrease
  • Slide 20
  • Another Way to show extremum First Derivative Test
  • Slide 21
  • Concavity
  • Slide 22
  • Graph
  • Slide 23
  • Appendix Differentiating & Simplifying
  • Slide 24
  • Example(1)
  • Slide 25
  • Slide 26
  • Example(2)
  • Slide 27
  • Slide 28
  • Example(3)
  • Slide 29
  • Slide 30
  • Slide 31
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