1
00:00:00;00 --> 00:00:06;06
Can you guys see? There
actually is a little rate

2
00:00:06;07 --> 00:00:08;13
of change that's right
here, but it's on the line,

3
00:00:08;14 --> 00:00:10;12
so what's the rate of
change over this interval?

4
00:00:10;13 --> 00:00:15;06
Zero. So, the rate of
change is zero over what

5
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interval of x? zero one.
Down here, from zero one,

6
00:00:21;06 --> 00:00:27;07
how much would y change
over that? Not at all. So

7
00:00:27;08 --> 00:00:30;05
that actually ends up
coming back down because

8
00:00:30;06 --> 00:00:33;04
its a rate of change of
zero. So then I'm going to

9
00:00:33;05 --> 00:00:35;07
look at the next step from
one to two,

10
00:00:35;08 --> 00:00:37;03
go back up here from one to two.

11
00:00:37;04 --> 00:00:39;13
What's the rate of change over this interval?

12
00:00:39;14 --> 00:00:40;11
[Half.]

13
00:00:40;12 --> 00:00:46;00
.5, a half. So in this next
step, interval size one,

14
00:00:46;01 --> 00:00:47;06
how much does y change?

15
00:00:47;07 --> 00:00:49;09
By .5

16
00:00:58;11 --> 00:01:03;00
In the next step, from 2 to
3, what's the rate of

17
00:01:30;01 --> 00:01:07;14
change from 2 to 3? Can you
see it? You can look at

18
00:01:07;15 --> 00:01:11;00
your own papers if mine is
too small. From 2 to 3,

19
00:01:11;01 --> 00:01:14;13
what is the rate of change?
One. For that whole

20
00:01:14;14 --> 00:01:18;09
interval, for this next
whole interval, the rate of

21
00:01:18;10 --> 00:01:22;02
change is one. So, as x
changes from 2 to 3, how

22
00:01:22;03 --> 00:01:27;11
much does y change? By one
more than where it already

23
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was. Because this is all
building on itself. For

24
00:01:31;13 --> 00:01:33;13
this interval, it didn't
change at all. For the next

25
00:01:33;14 --> 00:01:36;29
interval, it changed by .5,
for the next interval it

26
00:01:37;00 --> 00:01:40;03
changed by one. Tell me
where I should make my next

27
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dot. I know it'll be over
at 3,

28
00:01:42;02 --> 00:01:43;08
but what's the y value
going to be?

29
00:01:43;09 --> 00:01:45;07
[One point five.]

30
00:01:45;08 --> 00:01:46;04 One and a half. Good.

31
00:01:46;05 --> 00:02:10;05
There, we just did three of
them. You guys continue.