[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.95,0:00:03.32,Default,,0000,0000,0000,,두 번 미분할 수 있는 \N함수 g와
Dialogue: 0,0:00:03.32,0:00:07.23,Default,,0000,0000,0000,,이계도함수 g''의\N그래프를 그렸습니다
Dialogue: 0,0:00:07.23,0:00:08.79,Default,,0000,0000,0000,,여기에 보이죠
Dialogue: 0,0:00:08.79,0:00:10.80,Default,,0000,0000,0000,,이계도함수를\N이용해 정의하기라는
Dialogue: 0,0:00:10.80,0:00:12.44,Default,,0000,0000,0000,,칸아카데미의 글을 통해
Dialogue: 0,0:00:12.44,0:00:14.94,Default,,0000,0000,0000,,설명을 드리는 것입니다
Dialogue: 0,0:00:14.94,0:00:16.43,Default,,0000,0000,0000,,여기 함수 g를 봅시다
Dialogue: 0,0:00:16.43,0:00:18.24,Default,,0000,0000,0000,,이는 일계도함수가 아니라
Dialogue: 0,0:00:18.24,0:00:19.73,Default,,0000,0000,0000,,이계도함수입니다
Dialogue: 0,0:00:19.73,0:00:21.09,Default,,0000,0000,0000,,갈색으로 표시했죠
Dialogue: 0,0:00:21.09,0:00:23.50,Default,,0000,0000,0000,,해당 글에서는
Dialogue: 0,0:00:23.50,0:00:24.94,Default,,0000,0000,0000,,해당 글에서는
Dialogue: 0,0:00:24.94,0:00:27.36,Default,,0000,0000,0000,,네 명의 학생이\N함수 g가 x = -2에서
Dialogue: 0,0:00:27.36,0:00:30.50,Default,,0000,0000,0000,,변곡점을 가지는
Dialogue: 0,0:00:30.50,0:00:35.88,Default,,0000,0000,0000,,미적분학적 증명을\N하라고 합니다
Dialogue: 0,0:00:35.88,0:00:37.38,Default,,0000,0000,0000,,이는 직감적으로
Dialogue: 0,0:00:37.38,0:00:39.22,Default,,0000,0000,0000,,맞다고 생각이 됩니다
Dialogue: 0,0:00:39.22,0:00:40.34,Default,,0000,0000,0000,,x = -2일 경우
Dialogue: 0,0:00:40.34,0:00:42.41,Default,,0000,0000,0000,,변곡점이 무엇인지\N복습해봅시다
Dialogue: 0,0:00:42.42,0:00:43.94,Default,,0000,0000,0000,,이는 오목성이 아래에서
Dialogue: 0,0:00:43.94,0:00:45.60,Default,,0000,0000,0000,,위로 변하는 점입니다
Dialogue: 0,0:00:45.60,0:00:48.31,Default,,0000,0000,0000,,혹은 위에서 아래로 변하죠
Dialogue: 0,0:00:48.31,0:00:50.03,Default,,0000,0000,0000,,다른 말로 설명하면
Dialogue: 0,0:00:50.03,0:00:51.55,Default,,0000,0000,0000,,기울기가 감소에서 증가로
Dialogue: 0,0:00:51.55,0:00:54.22,Default,,0000,0000,0000,,혹은 증가에서 감소로
Dialogue: 0,0:00:54.22,0:00:56.33,Default,,0000,0000,0000,,변하는 점입니다
Dialogue: 0,0:00:56.33,0:00:57.97,Default,,0000,0000,0000,,여기서 이를 확인하면
Dialogue: 0,0:00:57.97,0:01:00.60,Default,,0000,0000,0000,,기울기가\N줄어들며 양수입니다
Dialogue: 0,0:01:00.60,0:01:02.59,Default,,0000,0000,0000,,하지만 줄어들며\N0에 도달합니다
Dialogue: 0,0:01:02.59,0:01:05.30,Default,,0000,0000,0000,,계속 줄어들며
Dialogue: 0,0:01:05.30,0:01:06.51,Default,,0000,0000,0000,,음수가 됩니다
Dialogue: 0,0:01:06.51,0:01:08.19,Default,,0000,0000,0000,,x = -2에 도달할 때까지
Dialogue: 0,0:01:08.19,0:01:09.18,Default,,0000,0000,0000,,감소합니다
Dialogue: 0,0:01:09.18,0:01:11.16,Default,,0000,0000,0000,,그 다음 다시 증가합니다
Dialogue: 0,0:01:11.16,0:01:13.41,Default,,0000,0000,0000,,그다음 음수가\N될 때까지 계속 감소합니다
Dialogue: 0,0:01:13.41,0:01:15.26,Default,,0000,0000,0000,,여기 0에 도달한 뒤
Dialogue: 0,0:01:15.26,0:01:17.40,Default,,0000,0000,0000,,계속 증가합니다
Dialogue: 0,0:01:17.40,0:01:18.77,Default,,0000,0000,0000,,계속 증가하며\N양수에 도달합니다
Dialogue: 0,0:01:18.77,0:01:22.17,Default,,0000,0000,0000,,결국 x = -2일 경우
Dialogue: 0,0:01:22.17,0:01:24.44,Default,,0000,0000,0000,,오목성이 위에서
Dialogue: 0,0:01:24.44,0:01:26.16,Default,,0000,0000,0000,,아래로 바뀝니다
Dialogue: 0,0:01:26.16,0:01:28.75,Default,,0000,0000,0000,,미적분학적 정의에 따르면
Dialogue: 0,0:01:28.75,0:01:31.39,Default,,0000,0000,0000,,이계도함수에선
Dialogue: 0,0:01:31.39,0:01:33.54,Default,,0000,0000,0000,,이계도함수가 x축을
Dialogue: 0,0:01:33.54,0:01:35.19,Default,,0000,0000,0000,,가로지르는\N부분을 봐야합니다
Dialogue: 0,0:01:35.19,0:01:37.81,Default,,0000,0000,0000,,왜냐하면\N이계도함수가 음수이면
Dialogue: 0,0:01:37.81,0:01:40.17,Default,,0000,0000,0000,,기울기가 감소합니다
Dialogue: 0,0:01:40.17,0:01:41.95,Default,,0000,0000,0000,,오목성이 아래쪽이죠
Dialogue: 0,0:01:41.95,0:01:43.95,Default,,0000,0000,0000,,이계도함수가 양수라면
Dialogue: 0,0:01:43.95,0:01:46.44,Default,,0000,0000,0000,,일계도함수가\N증가하는 것이고
Dialogue: 0,0:01:46.44,0:01:49.03,Default,,0000,0000,0000,,원래 함수의 기울기가
Dialogue: 0,0:01:49.03,0:01:50.67,Default,,0000,0000,0000,,증가하며 오목성이\N위를 향합니다
Dialogue: 0,0:01:50.67,0:01:53.68,Default,,0000,0000,0000,,따라서 x = -2에
Dialogue: 0,0:01:53.68,0:01:55.97,Default,,0000,0000,0000,,이계도함수가 x축을
Dialogue: 0,0:01:55.97,0:01:58.35,Default,,0000,0000,0000,,가로지르게 됩니다
Dialogue: 0,0:01:58.35,0:02:00.93,Default,,0000,0000,0000,,0에 도달하거나
Dialogue: 0,0:02:00.93,0:02:01.92,Default,,0000,0000,0000,,x축에 닿는 것이\N다가 아닙니다
Dialogue: 0,0:02:01.92,0:02:03.90,Default,,0000,0000,0000,,임계점을 찾으려면
Dialogue: 0,0:02:03.90,0:02:06.46,Default,,0000,0000,0000,,x축을 가로지르는\N점을 찾아야 합니다
Dialogue: 0,0:02:06.47,0:02:08.82,Default,,0000,0000,0000,,다음이 주어진 경우의
Dialogue: 0,0:02:08.82,0:02:10.76,Default,,0000,0000,0000,,학생들의 정의를 보고
Dialogue: 0,0:02:10.76,0:02:12.97,Default,,0000,0000,0000,,선생님이 된 기분으로
Dialogue: 0,0:02:12.97,0:02:14.70,Default,,0000,0000,0000,,각 정의에 따라
Dialogue: 0,0:02:14.70,0:02:16.04,Default,,0000,0000,0000,,선생님이 정의에 대해
Dialogue: 0,0:02:16.04,0:02:17.66,Default,,0000,0000,0000,,뭐라고 할지 생각해 봅시다
Dialogue: 0,0:02:17.66,0:02:20.02,Default,,0000,0000,0000,,첫 번째 학생은\Ng의 도함수는
Dialogue: 0,0:02:20.02,0:02:23.07,Default,,0000,0000,0000,,x = -2에서 부호를\N바꾼다고 합니다
Dialogue: 0,0:02:23.07,0:02:25.99,Default,,0000,0000,0000,,방금 저희가 말한 내용이죠
Dialogue: 0,0:02:25.99,0:02:29.00,Default,,0000,0000,0000,,이계도함수가 부호를 바꾼다면
Dialogue: 0,0:02:29.00,0:02:31.25,Default,,0000,0000,0000,,음수에서 양수로 바뀌며
Dialogue: 0,0:02:31.26,0:02:33.04,Default,,0000,0000,0000,,일계도함수는
Dialogue: 0,0:02:33.04,0:02:35.62,Default,,0000,0000,0000,,감소에서 증가로 바뀝니다
Dialogue: 0,0:02:35.62,0:02:39.08,Default,,0000,0000,0000,,그리고 이는 미적분학적
Dialogue: 0,0:02:39.08,0:02:41.04,Default,,0000,0000,0000,,정의에 해당합니다
Dialogue: 0,0:02:41.04,0:02:42.85,Default,,0000,0000,0000,,따라서 지금까지는\N맞게 풀었다는
Dialogue: 0,0:02:42.85,0:02:45.18,Default,,0000,0000,0000,,이 보기를 첫 번째\N학생에게 주겠습니다
Dialogue: 0,0:02:45.18,0:02:47.41,Default,,0000,0000,0000,,x축을 가로지릅니다
Dialogue: 0,0:02:47.41,0:02:49.44,Default,,0000,0000,0000,,이 증명은 애매하네요
Dialogue: 0,0:02:49.44,0:02:50.72,Default,,0000,0000,0000,,어떤 것이 x축을\N가로지르나요?
Dialogue: 0,0:02:50.72,0:02:51.91,Default,,0000,0000,0000,,만약 학생이 이와\N같은 증명을 적었다면
Dialogue: 0,0:02:51.91,0:02:52.94,Default,,0000,0000,0000,,어떤 것인지
Dialogue: 0,0:02:52.94,0:02:54.07,Default,,0000,0000,0000,,일계도함수인지
Dialogue: 0,0:02:54.07,0:02:55.69,Default,,0000,0000,0000,,이계도함수인지 물을 것입니다
Dialogue: 0,0:02:55.69,0:02:58.48,Default,,0000,0000,0000,,따라서 더 명확히\N표현하라고 할 것입니다
Dialogue: 0,0:02:58.48,0:03:01.23,Default,,0000,0000,0000,,이 정의는 올바르지 않습니다
Dialogue: 0,0:03:01.23,0:03:03.20,Default,,0000,0000,0000,,다른 보기를 봅시다
Dialogue: 0,0:03:03.20,0:03:05.24,Default,,0000,0000,0000,,이계도함수 g는
Dialogue: 0,0:03:05.24,0:03:08.38,Default,,0000,0000,0000,,x = -2일 경우
Dialogue: 0,0:03:08.38,0:03:09.56,Default,,0000,0000,0000,,증가합니다
Dialogue: 0,0:03:09.57,0:03:11.55,Default,,0000,0000,0000,,이 증명은 임계점이
Dialogue: 0,0:03:11.55,0:03:13.23,Default,,0000,0000,0000,,왜 여기에 있는지\N증명하지 않습니다
Dialogue: 0,0:03:13.23,0:03:14.52,Default,,0000,0000,0000,,예를 들어
Dialogue: 0,0:03:14.52,0:03:17.04,Default,,0000,0000,0000,,이계도함수는\Nx = -2.5일 경우
Dialogue: 0,0:03:17.04,0:03:20.28,Default,,0000,0000,0000,,증가합니다
Dialogue: 0,0:03:20.28,0:03:22.24,Default,,0000,0000,0000,,이계도함수는
Dialogue: 0,0:03:22.24,0:03:23.38,Default,,0000,0000,0000,,x = -1일 경우도
Dialogue: 0,0:03:23.38,0:03:24.40,Default,,0000,0000,0000,,증가합니다
Dialogue: 0,0:03:24.40,0:03:25.94,Default,,0000,0000,0000,,하지만 이 부분에서
Dialogue: 0,0:03:25.94,0:03:27.14,Default,,0000,0000,0000,,임계점을 가지지 않습니다
Dialogue: 0,0:03:27.14,0:03:29.10,Default,,0000,0000,0000,,따라서 이는 g가
Dialogue: 0,0:03:29.10,0:03:30.51,Default,,0000,0000,0000,,왜 임계점을 가지는지\N설명하지 않습니다
Dialogue: 0,0:03:30.51,0:03:33.60,Default,,0000,0000,0000,,마지막 학생은
Dialogue: 0,0:03:33.60,0:03:35.54,Default,,0000,0000,0000,,g의 그래프의 오목성이
Dialogue: 0,0:03:35.54,0:03:37.30,Default,,0000,0000,0000,,x = -2일 경우\N바뀐다고 합니다
Dialogue: 0,0:03:37.30,0:03:38.98,Default,,0000,0000,0000,,이는 참입니다
Dialogue: 0,0:03:38.98,0:03:42.19,Default,,0000,0000,0000,,하지만 미적분학적\N증명이 아니죠
Dialogue: 0,0:03:42.19,0:03:45.90,Default,,0000,0000,0000,,여기선 이계도함수를\N사용해야 합니다