Global Extrema (Absolute Max and Absolute Min)
Global Extrema or Absolute Extrema are similar to Local Extrema, but they are not exactly the same . An Absolute Extrema is wanting to know the largest y-value and the smallest y-value for the ENTIRE equation. Whereas Local Extrema want to know the largest and smallest y-values in their little part of the world, locally . Local Extrema are not necessarily the largest and smallest y-values for the full equation, only in their little section of a graph.
Definition: Global Extrema or Absolute Extrema
A Global Max(Absolute Max) is the largest y-value in an x-interval .
A Global Min (Absolute Min) is the smallest y-value in an x-interval .
The main difference between Absolute Extrema and Local Extrema, is that Absolute Extrema do not have to occur at peaks and valleys, and Absolute Extrema are generally asked about in terms of a closed x-interval , [ a , b ].
In this example you would have a local max at the peak and a local min at the valley, but that is not the location of the largest y-value , absolute max,and the smallest y-value , absolute min. The Absolute Extrema are occurring at the endpoints of the x-interval .
Keep in mind that Absolute Extrema can also occur in multiple places, x-values . You are only being asked what is the absolute largest or absolute smallest y-value of your given equation. There is no reason that those extreme y-values only have to happen once, at a single x-value , those absolute y-values can occur many times.
