Yes, it is not possible to have an absolute maximum or absolute minimum.
Here,
We are examining a function over an interval ( a , b ) , for a and b finite,
We have to find, is it possible not to have an absolute maximum or absolute minimum.
What theorem indicates the existence of absolute maxima or absolute minima of a function?
If f is continuous on a closed interval [a, b] (that is: on a closed and bounded interval), then, the Extreme Value Theorem indicates the existence of an absolute maximum or minimum value of f on the interval [a, b].
Now,
The function is define over an interval (a, b).
Hence, the function is define on open interval.
So, it is not possible to have an absolute maximum or absolute minimum.
Learn more about the existence of maxima and minima visit:
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