After completing this section, you should be able to do the following.

  • Define absolute maximum and absolute minimum.
  • Find the absolute maximum and minimum using a graph.
  • Define relative maximum and relative minimum.
  • Find relative maxima and minima using a graph.
  • Compare and contrast relative and absolute maxima and minima.
  • Given a graph without an absolute maximum or minimum, explain why the graph has no absolute maximum or minimum.
  • Given a graph without any extrema, explain why the graph has no extrema.
  • Identify situations in which a continuous function is guaranteed to have both an absolute maximum and minimum.