For this reason, the points A and C
may be regarded as points of local minimum value (or relative minimum value) and
points B and D may be regarded as points of local maximum value (or relative maximum
value) for the function The local maximum value and local minimum value of the
function are referred to as local maxima and local minima, respectively, of the function We now formally give the following definition
Definition 4 Let  f  be a real valued function and let c be an interior point in the domain
of f Then
(a)
c is called a point of local maxima if there is an h > 0 such that
f (c) ≥ f (x), for all x in (c – h, c + h), x ≠ c
The value f (c) is called the local maximum value of f