Here is the procedure for finding absolute extrema. After you have solved the equation f x 0 you have found the locations at which the extrema are located. If it changes from negative to positive it is a relative min.
Relative extrema maxs mins are sometimes called local extrema Other than just pointing these things out on the graph we have a very specific way to write them out.
If f x is continuous in a closed interval I then the absolute extrema of f x in I occur at the critical points andor at the endpoints of I. Officially for this graph wed say. If a critical point or endpoint changes from positive to negative it is a relative max. So when we talk about finding extrema on a closed range it means we need to consider high points and low points inside the interval plus the intervals endpoints.