WEBVTT
1
00:00:04.030 --> 00:00:06.240 A:middle L:90%
in this problem. We're looking for the point where
2
00:00:06.240 --> 00:00:09.769 A:middle L:90%
the Tanja line is perpendicular to the given line and
3
00:00:09.769 --> 00:00:13.519 A:middle L:90%
perpendicular lines have opposite reciprocal slopes. So let's find
4
00:00:13.519 --> 00:00:15.830 A:middle L:90%
the slope of the given line. Let's take this
5
00:00:15.830 --> 00:00:18.929 A:middle L:90%
equation and isolate why. So we'll subtract six x
6
00:00:18.929 --> 00:00:25.649 A:middle L:90%
from both sides and divide by two. So the
7
00:00:25.649 --> 00:00:28.699 A:middle L:90%
slope of this line is negative. Three. So
8
00:00:28.699 --> 00:00:32.039 A:middle L:90%
the perpendicular slope would be positive 1/3. So we're
9
00:00:32.039 --> 00:00:34.119 A:middle L:90%
looking for the point where the Tanja line has a
10
00:00:34.119 --> 00:00:37.039 A:middle L:90%
slope of 1/3. That means we want the derivative
11
00:00:37.039 --> 00:00:41.950 A:middle L:90%
to equal 1/3. So let's find the derivative.
12
00:00:42.549 --> 00:00:44.840 A:middle L:90%
I'm going to rewrite the function as one plus two
13
00:00:44.840 --> 00:00:47.899 A:middle L:90%
x to the 1/2 power and then I'm going to
14
00:00:47.899 --> 00:00:51.840 A:middle L:90%
use the chain rule. Why Prime equals 1/2 times
15
00:00:51.840 --> 00:00:54.579 A:middle L:90%
one plus two x to the negative 1/2 power that
16
00:00:54.579 --> 00:00:56.649 A:middle L:90%
takes care of the first part of the chain rule
17
00:00:57.090 --> 00:00:59.560 A:middle L:90%
times the derivative of the inside, which is to
18
00:01:00.520 --> 00:01:02.960 A:middle L:90%
now we can multiply the 1/2 of the two that
19
00:01:02.960 --> 00:01:04.700 A:middle L:90%
was canceled. And now we want this derivative to
20
00:01:04.700 --> 00:01:07.920 A:middle L:90%
be equal to 1/3 so this derivative could be written
21
00:01:07.920 --> 00:01:11.340 A:middle L:90%
as one over the square root of one plus two
22
00:01:11.340 --> 00:01:14.859 A:middle L:90%
x, and it equals 1/3. Let's take the
23
00:01:14.859 --> 00:01:17.359 A:middle L:90%
reciprocal of both sides, and we have a square
24
00:01:17.359 --> 00:01:19.370 A:middle L:90%
root of one plus two. X is equal to
25
00:01:19.370 --> 00:01:22.939 A:middle L:90%
three. Now it's square both sides, and we
26
00:01:22.939 --> 00:01:26.519 A:middle L:90%
have one plus two. X equals nine. Subtract
27
00:01:26.519 --> 00:01:29.430 A:middle L:90%
12 X equals eight and divide by two. X
28
00:01:29.430 --> 00:01:32.319 A:middle L:90%
equals four. Okay, this is the X coordinate
29
00:01:32.319 --> 00:01:34.780 A:middle L:90%
of the point. We also want the Y coordinate
30
00:01:34.780 --> 00:01:37.620 A:middle L:90%
of the point, and the Y coordinate would be
31
00:01:37.620 --> 00:01:40.019 A:middle L:90%
what we get when we take four and substituted into
32
00:01:40.019 --> 00:01:42.090 A:middle L:90%
the original equation. So we have one plus two
33
00:01:42.090 --> 00:01:46.599 A:middle L:90%
times for inside a square root square root of nine
34
00:01:46.599 --> 00:01:49.280 A:middle L:90%
is three. So the point we're looking for is
35
00:01:49.280 --> 00:01:49.450 A:middle L:90%
the 0.0.43