Is Extrema a Continuous Function?

1 states that a continuous function on a closed interval will have absolute extrema, that is, both an absolute maximum and an absolute minimum. These extrema occur either at the endpoints or at critical values in the interval.

Do extrema have to be continuous?

If a function is not continuous, then it may have absolute extrema at any points of discontinuity. Generally, absolute extrema will only be useful for functions with at most a finite number of points of discontinuity.

Do all continuous functions have extrema?

The second fact about continuous functions on closed intervals is that they always have global extrema (though they may not have local ones). absolute max and min.