Does the function
an absolute maximum and minimum on [-2, 1]
? How about on the
interval [0, )
This function does have an absolute maximum and minimum on the
interval [-2, 1], as predicted by the Max/Min theorem for continuous
functions. The absolute maximum is 1, and the absolute minimum
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
Thus, the boundedness condition in the Max/Min theorem for continuous
functions is essential.