Hi guys just wanted to clear up this notion of local/global extremum at an interior point. I would like to know what's the proper definition for a function having a local/global extremum.
I know a local extremum can be a maximum or minimum value while a global extremum can be the largest maximum or minimum value. As it relates , to defining it is there more to it or is this the general idea.
$f$ has a global maximum at $x$ if $f(y) \leq f(x)$, where $f(y$) is the function values.
The opposite is for the minimum where $f(x) \leq f(y)$ and for the minimum a neighborhood is considered in each instance within the function.