The lowest point on a graph is called theminima; the highest point on a graph is called themaxima. “Global means “the entire graph of the function” while “local” refers to “a small part of the graph”. Image Source: https://en.wikipedia.org/wiki/Maxima_and_minima ...
They are called “symmetric” not because their graph showssymmetry, but because they remain the same if you permute their roots. As far as graphing, the graph of any symmetric polynomial would look exactly the same no matter which variables you switch around. If the graph changes, then the ...