안녕하세요 이연욱 샘입니다.

질문:"왜 open interval일땐 extreme value theorem이 해당되지 않는지에 대한 두번째 예시 그래프를 설명해주실때, extreme values가 open circle인 (a,b)가 아닌 그래프 중간에 있다면 absolute minimum과 maximum이 있다고 하셨어요. 그런데 왜 그런 케이스에는 The extreme Values Theorem이 해당이 되지 않는건가요?"

대답: If a function is continuous on a open interval (a,b), it does NOT guarantee that the function has an absolute maximum and has an absolute minimum on a open interval (a,b), which implies that the function might have an absolute maximum and has an absolute minimum on a open interval (a,b) or it might NOT have an absolute maximum and has an absolute minimum on a open interval (a,b). However, according to the Extreme Value theorem, if a function is continuous on a closed interval [a,b], it guarantees that the function has an absolute maximum and has an absolute minimum on a closed interval [a,b].

질문에 도움이 되었으면 합니다. 감사합니다.