WEBVTT
1
00:00:01.040 --> 00:00:08.050 A:middle L:90%
all right. So derivative or function is given by
2
00:00:08.050 --> 00:00:09.929 A:middle L:90%
OK, X to the minus one half of her
3
00:00:09.929 --> 00:00:11.640 A:middle L:90%
ex mines three bomb is going to write that his
4
00:00:11.640 --> 00:00:17.949 A:middle L:90%
ex minus three over square root of X. Good
5
00:00:19.030 --> 00:00:23.390 A:middle L:90%
. Okay. And so if we're looking for a
6
00:00:23.390 --> 00:00:26.730 A:middle L:90%
critical points well, we see the X equals three
7
00:00:26.730 --> 00:00:31.949 A:middle L:90%
is going to make f prime undefined. And then
8
00:00:33.340 --> 00:00:36.340 A:middle L:90%
also, X equals zero X equals three is going
9
00:00:36.340 --> 00:00:39.140 A:middle L:90%
to make a private call zero Sorry. And then
10
00:00:39.140 --> 00:00:41.729 A:middle L:90%
X equals zero is gonna make of prime on to
11
00:00:41.729 --> 00:00:46.469 A:middle L:90%
find. So we need to consider those values.
12
00:00:47.289 --> 00:00:49.280 A:middle L:90%
Okay. And then we want to know where is
13
00:00:49.289 --> 00:00:55.259 A:middle L:90%
f increasing and decreasing. Well, fans era and
14
00:00:55.259 --> 00:00:58.429 A:middle L:90%
three, we can look enough crime to see where
15
00:00:58.429 --> 00:01:00.920 A:middle L:90%
l promise positive or negative Tell us where is increasing
16
00:01:00.920 --> 00:01:04.969 A:middle L:90%
or decreasing. So less than zero f crime was
17
00:01:04.969 --> 00:01:07.329 A:middle L:90%
going to be undefined because we'll be taking the square
18
00:01:07.329 --> 00:01:11.239 A:middle L:90%
root of a night, remember? And then between
19
00:01:11.239 --> 00:01:14.439 A:middle L:90%
zero and three it looks like the derivative is negative
20
00:01:15.340 --> 00:01:22.140 A:middle L:90%
. Good morning. And then, um let's see
21
00:01:22.370 --> 00:01:25.519 A:middle L:90%
between, uh, for ex greater than three,
22
00:01:25.780 --> 00:01:27.819 A:middle L:90%
the derivative is going to be positive. And so
23
00:01:27.819 --> 00:01:30.890 A:middle L:90%
it looks like our function no. Okay, he's
24
00:01:30.890 --> 00:01:34.590 A:middle L:90%
going to start at zero and it's going to be
25
00:01:34.599 --> 00:01:42.340 A:middle L:90%
decreasing between zero and three and then an increasing from
26
00:01:42.340 --> 00:01:48.930 A:middle L:90%
three to infinity and then or extreme A. It
27
00:01:48.930 --> 00:01:55.030 A:middle L:90%
looks like we have a local man and X equals
28
00:01:55.030 --> 00:01:57.980 A:middle L:90%
three and then no local Max because it never.
29
00:01:57.010 --> 00:02:00.739 A:middle L:90%
The function never changes from being increasing, decreasing and
30
00:02:00.739 --> 00:02:04.329 A:middle L:90%
only changes from seem decreasing to increasing it through It's
31
00:02:04.329 --> 00:02:04.950 A:middle L:90%
a local man.