# Real function/Local maximum and minimum/Definition

Local maximum

Suppose that is a subset and let

denote a
function.
We say that attains a * local maximum* in a point
,
if there exists some
,
such that for all
fulfilling
,
the estimate

holds. We say that attains a * local minimum* in a point
,
if there exists some
,
such that for all
fulfilling
,
the estimate

holds.