1  Maximum and Minimum Values of a Function in a Closed Interval
Let us consider a function  f  given by
f (x) = x + 2, x ∈ (0, 1)
Observe that the function is continuous on (0, 1) and neither has a maximum value
nor has a minimum value Further, we may note that the function even has neither a
local maximum value nor a local minimum value However, if we extend the domain of  f  to the closed interval [0, 1], then f still may
not have a local maximum (minimum) values but it certainly does have maximum value
3 = f (1) and minimum value 2 =  f (0) The maximum value 3 of f at x = 1 is called
absolute maximum value (global maximum or greatest value) of f on the interval
[0, 1]