1
00:00:00;00 --> 00:00:03;01
This rate of change graph,
that tells us it's going to

2
00:00:03;02 --> 00:00:05;13
take a turn, have
a vertex, at 1.

3
00:00:05;14 --> 00:00:08;04
[Everything up
there is positive,]

4
00:00:08;-5 --> 00:00:11;03
[but it's decreasing,
and then it's]

5
00:00:11;04 --> 00:00:13;01
[decreasing when it's
negative down here.]

6
00:00:13;02 --> 00:00:15;04
OK, so what does that mean
for the original curve?

7
00:00:15;05 --> 00:00:20;05
[That means at 1, it has
to, at the turning point,]

8
00:00:20;06 --> 00:00:21;09
[what's the turning
point called?]

9
00:00:21;10 --> 00:00:22;05
The vertex

10
00:00:22;06 --> 00:00:23;01
[Vertex? OK.]

11
00:00:23;02 --> 00:00:25;12
Just tell me again, I
think, I think you're OK,

12
00:00;25;13 --> 00:00:29;11
but tell me again how the
fact that it's positive all

13
00:00:29;12 --> 00:00:31;12
the way up until then, but
then negative after that.

14
00:00:31;13 --> 00:00:33;04
How that relates
again to your curve?

15
00:00:34;07 --> 00:00:42;03
[Because it's increasing
then it decreases.]

16
00:00:42;04 --> 00:00:44;12
[I don't know.
I don't know.]

17
00:00:46;07 --> 00:00:49;07
OK, so what does positive
rate of change. Does that

18
00:00:49;08 --> 00:00:52;04
[Oh yeah, because it's
positive, but then]

19
00:00:52;05 --> 00:00:53;13
[once it hits 1, it
starts going negative.]

20
00:00:53;14 --> 00:00:55;00
Which means a decrease

21
00:00:55;01 --> 00:00:55;05
[Yeah]

22
00:00:55;06 --> 00:00:57;03
OK, so that's why
it's your turning point.

23
00:00:57;04 --> 00:01:01;06
So, where it changes from
being positive to negative

24
00:01:01;07 --> 00:01:02;12
tells you where it
changes from being...

25
00:01:04;13 --> 00:01:05;13
[Increasing to decreasing]

26
00:01:05;14 --> 00:01:07;09
Exactly. That's why
it's a turning point.

27
00:01:07;10 --> 00:01:08;04
[OK]

28
00:01:08;05 --> 00:01:11;04
So, and that's the same
thing if you look up here,

29
00:01:11;05 --> 00:01:11;14
that happens up here.

30
00:01:11;15 --> 00:01:16;04
So what's so special
about this point then?

31
00:01:16;05 --> 00:01:20;02
[The line is only going
to pass through it]

32
00:01:20;03 --> 00:01:21;14
OK, and how...

33
00:01:21;15 --> 00:01:23;00
[Because that's 2
and that's 1]

34
00:01:23;01 --> 00:01:25;14
Right, but it always passes
through that turning point

35
00:01:25;15 --> 00:01:29;00
here is at 2 here is
at 1, but they're both

36
00:01:29;01 --> 00:01:30;05
[On the X]

37
00:01:30;06 --> 00:01:32;06
On the X-axis. They're
not positive, they're not

38
00:01:32;07 --> 00:01:34;10
negative, they're right
in the middle, which is?

39
00:01:34;12 --> 00:01:38;02
[The turning point?]

40
00:01:38;03 --> 00:01:39;09
Well, yeah, but at 1,

41
00:01:39;10 --> 00:01:40;11
is the rate of
change positive?

42
00:01:40;12 --> 00:01:42;10
[Yes. Oh, no.]

43
00:01:45;08 --> 00:01:46;04
[It's zero]

44
00:01:46;05 --> 00:01:48;11
Yeah, just before 1
it's positive,

45
00:01:48;12 --> 00:01:50;12
and just after 1 it's...

46
00:01:50;13 --> 00:01:51;07
[negative]

47
00:01:51;08 --> 00:01:53;12
Negative, but right at 1, right at that turning

48
00:01:53;13 --> 00:01:55;12
point, it's zero. So,

49
00:01:55;13 --> 00:01:55;12
you want to know when your
rate of change is what?

50
00:01:55;13 --> 00:01:59;01
[Zero]

51
00:01:59;02 --> 00:02:00;09
Yup