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Definition of local extrema :
\Functions can have "hills and valleys" places where they reach a minimum or maximum value.
\Definition of absolute extrema :
\The maximum or minimum over the entire function is called an "Absolute" or "Global" maximum or minimum.
\There is only one global maximum (and one global minimum) but there can be more than one local maximum or minimum.
\Now observe the graph :
\Point A is absolute minimum.
\Point B is absolute maximum.
\Point C is neither maximum nor minimum.
\Point D is relative minimum.
\Point E is relative maximum.
\Point F is relative minimum.
\Point G is neither maximum nor minimum.
\![\"\"](\"/userfiles/image/steps_images/solution.JPG\")
Point A is absolute minimum.
\Point B is absolute maximum.
\Point C is neither maximum nor minimum.
\Point D is relative minimum.
\Point E is relative maximum.
\Point F is relative minimum.
\Point G is neither maximum nor minimum.