[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.24,0:00:04.42,Default,,0000,0000,0000,,c 小题，假设 y 等于 f(x) 是微分方程
Dialogue: 0,0:00:04.42,0:00:07.04,Default,,0000,0000,0000,,在初始条件 f(2) = 3 时的特解。
Dialogue: 0,0:00:07.04,0:00:11.49,Default,,0000,0000,0000,,
Dialogue: 0,0:00:11.49,0:00:15.71,Default,,0000,0000,0000,,那么 f 在 x 等于 2 处是局部极大值？
Dialogue: 0,0:00:15.71,0:00:18.77,Default,,0000,0000,0000,,还是局部极小值？或者都不是？
Dialogue: 0,0:00:18.77,0:00:20.89,Default,,0000,0000,0000,,验证你的结论。
Dialogue: 0,0:00:20.89,0:00:22.20,Default,,0000,0000,0000,,好的，若要考虑
Dialogue: 0,0:00:22.20,0:00:24.26,Default,,0000,0000,0000,,局部极小或极大值，
Dialogue: 0,0:00:24.26,0:00:26.71,Default,,0000,0000,0000,,可以看看这一点的导数。
Dialogue: 0,0:00:26.71,0:00:28.63,Default,,0000,0000,0000,,如果等于 0，那么这里就有可能是
Dialogue: 0,0:00:28.63,0:00:30.06,Default,,0000,0000,0000,,
Dialogue: 0,0:00:30.06,0:00:32.55,Default,,0000,0000,0000,,有可能是局部极大或极小值，
Dialogue: 0,0:00:32.55,0:00:34.75,Default,,0000,0000,0000,,如果不等于 0，那么都不是。
Dialogue: 0,0:00:34.75,0:00:36.11,Default,,0000,0000,0000,,而如果确实等于 0，
Dialogue: 0,0:00:36.11,0:00:37.70,Default,,0000,0000,0000,,我们还要判断是极大值还是极小值，
Dialogue: 0,0:00:37.70,0:00:40.84,Default,,0000,0000,0000,,看看二阶导数算出来是正是负，就能判断。
Dialogue: 0,0:00:40.84,0:00:42.36,Default,,0000,0000,0000,,我们回到这一题，
Dialogue: 0,0:00:42.36,0:00:45.68,Default,,0000,0000,0000,,我们要计算 f'
Dialogue: 0,0:00:45.68,0:00:49.31,Default,,0000,0000,0000,,我们要计算的是 f'——
Dialogue: 0,0:00:49.31,0:00:53.14,Default,,0000,0000,0000,,f'(2) 等于什么。
Dialogue: 0,0:00:53.14,0:00:56.71,Default,,0000,0000,0000,,那么我们知道 f'(x)
Dialogue: 0,0:00:56.71,0:01:01.58,Default,,0000,0000,0000,,f'(x)，也就是 dy/dx，
Dialogue: 0,0:01:01.58,0:01:05.00,Default,,0000,0000,0000,,它等于 2x 减 y。
Dialogue: 0,0:01:05.00,0:01:06.98,Default,,0000,0000,0000,,从上一题就能看到。
Dialogue: 0,0:01:06.98,0:01:10.03,Default,,0000,0000,0000,,所以 f'(2)，我这样写
Dialogue: 0,0:01:10.03,0:01:14.18,Default,,0000,0000,0000,,f'(2) 就等于
Dialogue: 0,0:01:14.18,0:01:16.06,Default,,0000,0000,0000,,2 乘以 2，
Dialogue: 0,0:01:16.06,0:01:19.12,Default,,0000,0000,0000,,2 乘以 2 减去
Dialogue: 0,0:01:19.12,0:01:21.76,Default,,0000,0000,0000,,x 等于 2 时 y 的值。
Dialogue: 0,0:01:21.76,0:01:24.67,Default,,0000,0000,0000,,我们知道 x 等于 2 时 y 的值吗？
Dialogue: 0,0:01:24.67,0:01:26.87,Default,,0000,0000,0000,,当然，这里已经给出了。
Dialogue: 0,0:01:26.87,0:01:29.06,Default,,0000,0000,0000,,y 等于 f(x)，
Dialogue: 0,0:01:29.06,0:01:31.03,Default,,0000,0000,0000,,当 x 等于 2，
Dialogue: 0,0:01:31.03,0:01:32.66,Default,,0000,0000,0000,,当 x 等于 2 时，
Dialogue: 0,0:01:32.66,0:01:35.20,Default,,0000,0000,0000,,y 等于 3，
Dialogue: 0,0:01:35.20,0:01:37.94,Default,,0000,0000,0000,,所以是 2 乘以 2 减 3。
Dialogue: 0,0:01:37.94,0:01:40.65,Default,,0000,0000,0000,,那么它就等于 4 减 3，等于 1
Dialogue: 0,0:01:40.65,0:01:42.13,Default,,0000,0000,0000,,
Dialogue: 0,0:01:42.13,0:01:47.13,Default,,0000,0000,0000,,由于在 2 点的导数不等于 0，
Dialogue: 0,0:01:47.19,0:01:50.08,Default,,0000,0000,0000,,所以它就不是极小值，局部极小值，
Dialogue: 0,0:01:50.08,0:01:53.11,Default,,0000,0000,0000,,也不是局部极大值，
Dialogue: 0,0:01:53.11,0:01:58.11,Default,,0000,0000,0000,,所以可以说，由于 f'(2)
Dialogue: 0,0:01:59.24,0:02:02.51,Default,,0000,0000,0000,,f'(2) 不等于 0，
Dialogue: 0,0:02:02.51,0:02:07.41,Default,,0000,0000,0000,,这个，我们说 f，\N我这样写，
Dialogue: 0,0:02:07.41,0:02:12.41,Default,,0000,0000,0000,,f 在 x 等于 2 处，既没达到极小值，
Dialogue: 0,0:02:14.11,0:02:16.27,Default,,0000,0000,0000,,局部极小值，这样说更好，
Dialogue: 0,0:02:16.27,0:02:19.54,Default,,0000,0000,0000,,局部极小，
Dialogue: 0,0:02:19.54,0:02:23.04,Default,,0000,0000,0000,,也没有达到局部极大值。
Dialogue: 0,0:02:23.04,0:02:26.32,Default,,0000,0000,0000,,
Dialogue: 0,0:02:26.32,0:02:29.06,Default,,0000,0000,0000,,好的，下一题。
Dialogue: 0,0:02:29.06,0:02:32.94,Default,,0000,0000,0000,,计算常数 m 和 b 的值，
Dialogue: 0,0:02:32.94,0:02:37.49,Default,,0000,0000,0000,,使得 y 等于 mx 加 b 是微分方程的一个解
Dialogue: 0,0:02:37.49,0:02:39.58,Default,,0000,0000,0000,,
Dialogue: 0,0:02:39.58,0:02:41.90,Default,,0000,0000,0000,,这道题有趣
Dialogue: 0,0:02:41.90,0:02:44.08,Default,,0000,0000,0000,,我们来，这样吧，\N我们先把所有已知条件都写下来
Dialogue: 0,0:02:44.08,0:02:47.26,Default,,0000,0000,0000,,然后再考虑 y 等于 mx 加 b
Dialogue: 0,0:02:47.26,0:02:49.90,Default,,0000,0000,0000,,是微分方程的一个解这个条件。
Dialogue: 0,0:02:49.90,0:02:54.51,Default,,0000,0000,0000,,我们已经知道，
Dialogue: 0,0:02:54.51,0:02:58.94,Default,,0000,0000,0000,,dy/dx 等于 2x 减 y，
Dialogue: 0,0:02:58.94,0:03:00.27,Default,,0000,0000,0000,,是已知条件。
Dialogue: 0,0:03:00.27,0:03:02.28,Default,,0000,0000,0000,,我们也知道二阶导数，
Dialogue: 0,0:03:02.28,0:03:07.28,Default,,0000,0000,0000,,y 对 x 的二阶导数，等于
Dialogue: 0,0:03:07.52,0:03:12.52,Default,,0000,0000,0000,,2 减 dy/dx，
Dialogue: 0,0:03:12.82,0:03:14.33,Default,,0000,0000,0000,,这是我们在 b 小题中得出的结论。
Dialogue: 0,0:03:14.33,0:03:17.27,Default,,0000,0000,0000,,那么，我们可以将它表示成
Dialogue: 0,0:03:17.27,0:03:18.91,Default,,0000,0000,0000,,我们看，可以写为
Dialogue: 0,0:03:18.91,0:03:22.60,Default,,0000,0000,0000,,2 减 2x 加 y，通过代换
Dialogue: 0,0:03:22.60,0:03:25.38,Default,,0000,0000,0000,,就是把它代换进来
Dialogue: 0,0:03:25.38,0:03:27.83,Default,,0000,0000,0000,,那么这是 2 减 2x 加 y，
Dialogue: 0,0:03:27.83,0:03:29.28,Default,,0000,0000,0000,,我这么写，
Dialogue: 0,0:03:29.28,0:03:33.60,Default,,0000,0000,0000,,
Dialogue: 0,0:03:33.60,0:03:35.78,Default,,0000,0000,0000,,
Dialogue: 0,0:03:35.78,0:03:39.08,Default,,0000,0000,0000,,
Dialogue: 0,0:03:39.08,0:03:42.19,Default,,0000,0000,0000,,
Dialogue: 0,0:03:42.19,0:03:44.51,Default,,0000,0000,0000,,
Dialogue: 0,0:03:44.51,0:03:48.92,Default,,0000,0000,0000,,
Dialogue: 0,0:03:48.92,0:03:50.55,Default,,0000,0000,0000,,
Dialogue: 0,0:03:50.55,0:03:54.100,Default,,0000,0000,0000,,
Dialogue: 0,0:03:54.100,0:03:57.36,Default,,0000,0000,0000,,
Dialogue: 0,0:03:57.36,0:04:00.01,Default,,0000,0000,0000,,
Dialogue: 0,0:04:00.01,0:04:01.58,Default,,0000,0000,0000,,
Dialogue: 0,0:04:01.58,0:04:02.84,Default,,0000,0000,0000,,
Dialogue: 0,0:04:02.84,0:04:03.65,Default,,0000,0000,0000,,
Dialogue: 0,0:04:03.65,0:04:06.86,Default,,0000,0000,0000,,
Dialogue: 0,0:04:06.86,0:04:09.46,Default,,0000,0000,0000,,
Dialogue: 0,0:04:09.46,0:04:12.16,Default,,0000,0000,0000,,
Dialogue: 0,0:04:12.16,0:04:14.23,Default,,0000,0000,0000,,
Dialogue: 0,0:04:14.23,0:04:16.07,Default,,0000,0000,0000,,
Dialogue: 0,0:04:16.07,0:04:19.18,Default,,0000,0000,0000,,
Dialogue: 0,0:04:19.18,0:04:21.01,Default,,0000,0000,0000,,
Dialogue: 0,0:04:21.01,0:04:23.55,Default,,0000,0000,0000,,
Dialogue: 0,0:04:23.55,0:04:25.58,Default,,0000,0000,0000,,
Dialogue: 0,0:04:25.58,0:04:28.59,Default,,0000,0000,0000,,
Dialogue: 0,0:04:28.59,0:04:31.35,Default,,0000,0000,0000,,
Dialogue: 0,0:04:31.35,0:04:33.89,Default,,0000,0000,0000,,
Dialogue: 0,0:04:33.89,0:04:37.32,Default,,0000,0000,0000,,
Dialogue: 0,0:04:37.32,0:04:41.23,Default,,0000,0000,0000,,
Dialogue: 0,0:04:41.23,0:04:45.39,Default,,0000,0000,0000,,
Dialogue: 0,0:04:45.39,0:04:50.20,Default,,0000,0000,0000,,
Dialogue: 0,0:04:50.20,0:04:55.20,Default,,0000,0000,0000,,
Dialogue: 0,0:04:55.55,0:04:57.95,Default,,0000,0000,0000,,
Dialogue: 0,0:04:57.95,0:05:00.81,Default,,0000,0000,0000,,
Dialogue: 0,0:05:00.81,0:05:03.45,Default,,0000,0000,0000,,
Dialogue: 0,0:05:03.45,0:05:05.54,Default,,0000,0000,0000,,
Dialogue: 0,0:05:05.54,0:05:08.32,Default,,0000,0000,0000,,
Dialogue: 0,0:05:08.32,0:05:12.15,Default,,0000,0000,0000,,
Dialogue: 0,0:05:12.15,0:05:13.72,Default,,0000,0000,0000,,
Dialogue: 0,0:05:13.72,0:05:15.22,Default,,0000,0000,0000,,
Dialogue: 0,0:05:15.22,0:05:16.03,Default,,0000,0000,0000,,
Dialogue: 0,0:05:16.03,0:05:19.01,Default,,0000,0000,0000,,
Dialogue: 0,0:05:19.01,0:05:22.30,Default,,0000,0000,0000,,
Dialogue: 0,0:05:22.30,0:05:25.12,Default,,0000,0000,0000,,
Dialogue: 0,0:05:25.12,0:05:30.12,Default,,0000,0000,0000,,
Dialogue: 0,0:05:30.83,0:05:34.94,Default,,0000,0000,0000,,
Dialogue: 0,0:05:34.94,0:05:38.16,Default,,0000,0000,0000,,
Dialogue: 0,0:05:38.16,0:05:40.93,Default,,0000,0000,0000,,
Dialogue: 0,0:05:40.93,0:05:43.50,Default,,0000,0000,0000,,
Dialogue: 0,0:05:43.50,0:05:46.28,Default,,0000,0000,0000,,
Dialogue: 0,0:05:46.28,0:05:48.69,Default,,0000,0000,0000,,
Dialogue: 0,0:05:48.69,0:05:52.53,Default,,0000,0000,0000,,
Dialogue: 0,0:05:52.53,0:05:56.46,Default,,0000,0000,0000,,
Dialogue: 0,0:05:56.46,0:05:58.32,Default,,0000,0000,0000,,
Dialogue: 0,0:05:58.32,0:06:01.34,Default,,0000,0000,0000,,
Dialogue: 0,0:06:01.34,0:06:05.15,Default,,0000,0000,0000,,
Dialogue: 0,0:06:05.15,0:06:07.33,Default,,0000,0000,0000,,
Dialogue: 0,0:06:07.33,0:06:09.97,Default,,0000,0000,0000,,
Dialogue: 0,0:06:09.97,0:06:10.95,Default,,0000,0000,0000,,
Dialogue: 0,0:06:10.95,0:06:14.57,Default,,0000,0000,0000,,
Dialogue: 0,0:06:14.57,0:06:16.82,Default,,0000,0000,0000,,
Dialogue: 0,0:06:16.82,0:06:19.72,Default,,0000,0000,0000,,
Dialogue: 0,0:06:19.72,0:06:21.76,Default,,0000,0000,0000,,
Dialogue: 0,0:06:21.76,0:06:24.00,Default,,0000,0000,0000,,
Dialogue: 0,0:06:24.00,0:06:26.01,Default,,0000,0000,0000,,
Dialogue: 0,0:06:26.01,0:06:28.26,Default,,0000,0000,0000,,
Dialogue: 0,0:06:28.26,0:06:29.65,Default,,0000,0000,0000,,
Dialogue: 0,0:06:29.65,0:06:32.34,Default,,0000,0000,0000,,
Dialogue: 0,0:06:32.34,0:06:35.70,Default,,0000,0000,0000,,
Dialogue: 0,0:06:35.70,0:06:37.06,Default,,0000,0000,0000,,
Dialogue: 0,0:06:37.06,0:06:39.87,Default,,0000,0000,0000,,
Dialogue: 0,0:06:39.87,0:06:42.12,Default,,0000,0000,0000,,
Dialogue: 0,0:06:42.12,0:06:44.57,Default,,0000,0000,0000,,
Dialogue: 0,0:06:44.57,0:06:47.67,Default,,0000,0000,0000,,
Dialogue: 0,0:06:47.67,0:06:49.67,Default,,0000,0000,0000,,
Dialogue: 0,0:06:49.67,0:06:52.16,Default,,0000,0000,0000,,
Dialogue: 0,0:06:52.16,0:06:54.48,Default,,0000,0000,0000,,
Dialogue: 0,0:06:54.48,0:06:59.26,Default,,0000,0000,0000,,
Dialogue: 0,0:06:59.26,0:07:01.14,Default,,0000,0000,0000,,
Dialogue: 0,0:07:01.14,0:07:02.72,Default,,0000,0000,0000,,
Dialogue: 0,0:07:02.72,0:07:05.63,Default,,0000,0000,0000,,
Dialogue: 0,0:07:05.63,0:07:07.03,Default,,0000,0000,0000,,
Dialogue: 0,0:07:07.03,0:07:09.26,Default,,0000,0000,0000,,
Dialogue: 0,0:07:09.26,0:07:11.30,Default,,0000,0000,0000,,
Dialogue: 0,0:07:11.30,0:07:14.36,Default,,0000,0000,0000,,
Dialogue: 0,0:07:14.36,0:07:17.72,Default,,0000,0000,0000,,
Dialogue: 0,0:07:17.72,0:07:20.40,Default,,0000,0000,0000,,
Dialogue: 0,0:07:20.40,0:07:22.73,Default,,0000,0000,0000,,
Dialogue: 0,0:07:22.73,0:07:25.55,Default,,0000,0000,0000,,
Dialogue: 0,0:07:25.55,0:07:28.20,Default,,0000,0000,0000,,
Dialogue: 0,0:07:28.20,0:07:33.20,Default,,0000,0000,0000,,
Dialogue: 0,0:07:33.27,0:07:36.67,Default,,0000,0000,0000,,
Dialogue: 0,0:07:36.67,0:07:39.17,Default,,0000,0000,0000,,
Dialogue: 0,0:07:39.17,0:07:42.68,Default,,0000,0000,0000,,
Dialogue: 0,0:07:42.68,0:07:46.27,Default,,0000,0000,0000,,
Dialogue: 0,0:07:46.27,0:07:49.24,Default,,0000,0000,0000,,
Dialogue: 0,0:07:49.24,0:07:51.20,Default,,0000,0000,0000,,
Dialogue: 0,0:07:51.20,0:07:53.57,Default,,0000,0000,0000,,
Dialogue: 0,0:07:53.57,0:07:55.36,Default,,0000,0000,0000,,
Dialogue: 0,0:07:55.36,0:07:57.40,Default,,0000,0000,0000,,
Dialogue: 0,0:07:57.40,0:07:59.73,Default,,0000,0000,0000,,