Extrema : Note as well that while we say an "open interval around x = c " we mean that we can discover some interval ( a, b ) , not involving the endpoints, such that a < c < b . Or, in other terms, c will be contained somewhere within the interval and will not be either of the endpoints.
Also, we will collectively call the minimum and maximum points of a function the extrema of the function. Thus, relative extrema will refer to the relative minimums & maximums whereas absolute extrema refer to the absolute minimums & maximums.