Endpoints of an interval can be classified as local extrema depending on the specific definitions used in a mathematical context. While some definitions assert that endpoints cannot be considered local extrema, others allow for this classification if the endpoints are included in the interval. For example, in the case of the interval notation a < x < b, the endpoints a and b are excluded, thus disqualifying them as local maxima or minima. It is essential for students to consult their instructors for the applicable definitions relevant to their coursework.
PREREQUISITESStudents studying calculus, mathematics educators, and anyone seeking clarity on the classification of local extrema in relation to interval endpoints.
There's some debate over this issue. Many definitions indicate that endpoints canNOT be local (relative) extrema. However, there are also many definitions that indicate otherwise, so you should check with your teacher on the specific definition to be used for your class.blue_soda025 said:I'm kind of confused about whether or not an endpoint of an interval could also be a local extreme value. According to my textbook, it's true, but on the review sheets, the answers never included endpoints as local extrema. So can endpoints be local extrema?