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Intro to Extrema definitions

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  • Extrema
    Highest or lowest points on a function, including both overall and within specific regions.
  • Global Extrema
    Highest or lowest values across the entire function, considering all possible input values.
  • Absolute Extrema
    Alternative name for the highest or lowest points over the whole function.
  • Local Extrema
    Highest or lowest values within a small region of a function, not necessarily overall.
  • Relative Extrema
    Alternative name for the highest or lowest points within a specific region of a function.
  • Global Maximum
    Point where the function reaches its highest value compared to all other points.
  • Global Minimum
    Point where the function reaches its lowest value compared to all other points.
  • Local Maximum
    Point higher than all nearby points, but not necessarily the highest overall.
  • Local Minimum
    Point lower than all nearby points, but not necessarily the lowest overall.
  • Endpoint
    Boundary value of a function's domain, which may be a global extremum but not a local one by course convention.
  • Ordered Pair
    Notation (x, y) used to specify the location of extrema on a graph.
  • Peak
    Graph feature representing a local or global maximum, visually the highest point in a region.
  • Valley
    Graph feature representing a local or global minimum, visually the lowest point in a region.
  • Convention
    Agreed-upon rule or standard, such as whether endpoints count as local extrema.