1
00:00:00;00 --> 00:00:02;10
Let's see, at
negative 1, poof,

2
00:00:02;11 --> 00:00:03;10
there's our rate of change.

3
00:00:03;11 --> 00:00:05;08
Is that a positive or a
negative rate of change?

4
00:00:06;12 --> 00:00:09;07
[Positive]

5
00:00:09;10 --> 00:00:12;10
It's positive. I know what
you're getting confused in

6
00:00:12;11 --> 00:00:15;04
your head, and we'll talk
about it. At negative 1

7
00:00:15;05 --> 00:00:18;06
comma blah, there's your
rate of change. That's a

8
00:00:18;07 --> 00:00:20;01
positive number. If I were to write down that ordered

9
00:00:20;02 --> 00:00:22;13
pair, it would be negative
1 comma positive something.

10
00:00:22;14 --> 00:00:26;12
This is a positive rate of
change. What about at a

11
00:00:26;13 --> 00:00:29;13
half? Is that a positive
rate of change? Yeah, but

12
00:00:29;14 --> 00:00:32;00
compared to the rate of
change back here, is it

13
00:00:32;01 --> 00:00:33;10
just as positive
or less positive?

14
00:00:33;11 --> 00:00:34;09
[less positive]

15
00:00:34;10 --> 00:00:36;08
Less positive. I think
that's what you're kind of

16
00:00;36;09 --> 00:00:37;14
getting in your head.
You're like, well, it's

17
00:00:37;15 --> 00:00:40;01
decreasing, but it's
positive, does that make

18
00:00:40;02 --> 00:00:43;13
sense? It's just that it is
positive this whole time,

19
00:00:43;14 --> 00:00:46;07
so in terms of the original
curve, what does a positive

20
00:00:46;08 --> 00:00:50;07
rate of change mean? Will
my curve be increasing or

21
00:00:50;08 --> 00:00:52;14
decreasing over this
whole interval up until 1?

22
00:00:52;15 --> 00:00:54;00
[Increasing]

23
00:00:54;01 --> 00:00:57;09
Increasing. But is it
increasing at a quicker or

24
00:00:57;10 --> 00:00:59;13
slower rate as
X varies more

25
00:00:59;14 --> 00:01:02;01
[Slower]

26
00:01:02;02 --> 00:01:04;12
Slower, exactly. That's
what the fact that this is

27
00:01:04;13 --> 00:01:07;13
a negative rate of change
tells you. It's positive

28
00:01:07;14 --> 00:01:10;11
this whole time, but it's
getting less, and less, and

29
00:01:10;12 --> 00:01:13;03
less positive because
what happens after 1?

30
00:01:13;04 --> 00:01:16;13
It goes negative

31
00:01:16;14 --> 00:01:19;04
Exactly. The rate of
change goes negative,

32
00:01:19;05 --> 00:01:20;09
so your curve will do what?

33
00:01:20;10 --> 00:01:21;08
[Decrease]

34
00:01:21;09 --> 00:01:25;10
Decrease, exactly. Exactly.
Positive, positive,

35
00:01:25;11 --> 00:01:29;01
positive, so increase,
increase, increase, but

36
00:01:29;02 --> 00:01:33;12
increasing less and less,
right? You guys see that?

37
00:01:33;13 --> 00:01:36;11
Again, if you think about
what's going to happen

38
00:01:36;12 --> 00:01:40;00
after this X value of 1,
Katie said, my curve is

39
00:01:40;01 --> 00:01:42;10
going to start to decrease.
Well, if it changes from

40
00:01:42;11 --> 00:01:45;08
increase to decrease, it's
got to eventually do that

49
00:01:45;09 --> 00:01:48;01
level off thing, like she
said. It gets less and less

50
00:01:48;02 --> 00:01:52;11
positive. That's good. This
one starts out increasing

51
00:01:52;12 --> 00:01:55;10
and then changes to
decreasing, and where does

52
00:01:55;11 --> 00:01:57;14
that change happen in
this case? Kimmie?

53
00:01:59;03 --> 00:01:59;13
What did you say?

54
00:01:59;14 --> 00:02:00;13
Where does the
change happen

55
00:02:00;14 --> 00:02:03;10
in this case from an
increase to a decrease?

56
00:02:03;11 --> 00:02:05;04
At 1

57
00:02:05;05 --> 00:02:08;08
At 1, exactly. That change
that's going to take place

58
00:02:08;09 --> 00:02:12;09
on this curve will happen
at 1. In this case it's a

59
00:02:12;10 --> 00:02:15;07
change from increase
to decrease.