Interactive Real Analysis
- part of Examples 6.4.7(b):
Does the function 
have
an absolute maximum and minimum on [-2, 1] ? How about on the
interval [0, 
)
?
Back
have
an absolute maximum and minimum on [-2, 1] ? How about on the
interval [0, )
?
Back
On the other hand, on the unbounded interval [0, )
the function fails to possess both absolute maximum and minimum.
While 1 is still the absolute maximum, there no longer is an absolute
minimum.
Thus, the boundedness condition in the Max/Min theorem for continuous functions is essential.