1
00:00:02;10 --> 00:00:04;14
Essentially you're going
to start going backwards.

2
00:00:04;15 --> 00:00:08;10
I already gave you the
curve and I want you guys

3
00:00:08;11 --> 00:00:11;08
To estimate the rate of
change over certain

4
00:00:11;09 --> 00:00:15;04
Intervals. We'll start kind of
basic, and we'll do a few

5
00:00:15;05 --> 00:00:19;13
Different directions of
interval size 1. So, it's not

6
00:00:19;14 --> 00:00:22;01
Going to be the most
accurate thing in the whole

7
00:00:22;02 --> 00:00:24;05
Wide world, as we've
already seen how that gets

8
00:00:24;06 --> 00:00:27;07
Effected. But it will be a start.
Interval size of 1.

9
00:00:27;08 --> 00:00:32;06
Let's do this from negative
4 to positive 4.

10
00:00:32;07 --> 00:00:36;00
Essentially what you're
going to do is, back in the

10
00:00:36;01 --> 0:00:40;10
Day, first of all, rate of
change. Who remembers

11
00:00:40;11 --> 00:00:45;06
How rate of change works
in respect to changes in X's

12
00:00:45;07 --> 00:00:47;09
And changes in Y's? How
do we write rate of change?

13
00:00:53;04 --> 00:01:05;07
Change in who over
change in who. Samantha?

14
00:01:05;08 --> 00:01:07;03
[Change in Y over
change in X.]

15
00:01:07;04 --> 00:01:09;04
It is change in Y
over change in X.

16
00:01:10;05 --> 00:01:13;02
[Why does it matter
what you put where?]

17
00:01:15;13 --> 0:01:17;11
You know how we always
say that fundamental

18
00:01:17;12 --> 00:01:20;02
Phrase for every change
in X, Y changes how?

19
00:01:20;03 --> 00:01:24;08
So many times as
much, that's why.

20
00:01:25;06 --> 00:01:28;11
It's just the nature of rate of
change. Y changes with

21
00:01:28;12 --> 00:01:32;07
Respect to X, so Y changes
according to how X

22
00:01:32;08 --> 00:01:35;05
Changes. That's why.
Thank you for asking.

23
00:01:35;06 --> 00:01:42:05
Again, already given the
curve, step size of 1, going

24
00:01:42;06 --> 00:01:51;09
From negative 4 to 4. So,
starting at negative 4, so .1.

25
00:01:51;08 --> 00:01:54;13
Start at negative 4,
negative 4 what?

26
00:01:54;14 --> 00:01:57;02
You guys can probably see
it much better than I can,

27
00:01:57;03 --> 00:01:59;06
But what is the point that
corresponds with the X

28
00:01:59;07 --> 00:02:04;05
Value at negative 4? Negative 4 comma?

29
00:02:04;04 --> 00:02:04;12
[15]

30
00:02:04;15 --> 00:02:05;14
[Yeah]

32
00:02:06;00 --> 00:02:06;13
[20]

33
00:02:09;10 --> 00:02:10;07
[15]

34
00:02:14;10 --> 00:02:16;02
[20 is 2 plus]

35
00:02:16;03 --> 00:02:17;09
20 is too far away

36
00:02:19;00 --> 00:02:20;01
[I'm thinking 17]

37
00:02:21;15 --> 00:02:22;08
[I pick 19]

38
00:02:22;09 --> 00:02:23;09
[16]

39
00:02:23;10 --> 00:02:33;02
Let's take 16. And then
we're going to the next

40
00:02:33;03 --> 00:02:36;02
Point at interval size 1, so
I'm going from negative 4

41
00:02:36;02 --> 00:02:43;08
The next step will take
me to negative 3, exactly.

42
00:02;43;09 --> 00:02:44;12
Because you're going to do
a step size of 1, like I said.

43
00:02:44;12 --> 00:02:47;13
Go to your graph, look
carefully. What's going on

44
00:02:47;13 --> 00:02:50;02
At negative 3?
Follow it closely.

45
00:02:56;10 --> 00:02:58;07
I hear anywhere
from 8 to 9 to 10.

46
00:02:58;07 --> 00:02:59;11
Want to check the
middle and say 9?

47
00:02:59;12 --> 00:03:00;04
[9]

48
00:03:00;11 --> 00:03:07;14
9 it is. Here's the thing- the
way you guys did this graph

49
00:03:07;15 --> 00:03:11;09
For today, and again, your
graph is better than mine

50
00:03:11;10 --> 00:03:14;04
Because it's actually
bigger, it's ironic because

51
00:03:14;05 --> 00:03:17;01
It should be bigger on
my screen, but it's not.

52
00:03:17;02 --> 00:03:20;06
Your graph actually looks
bigger than mine. But

53
00:03:20;07 --> 00:03:22;12
You can do your rate of
change however you want.

54
00:03:22;13 --> 00:03:27;03
Remember back in the day
we did, we called them

55
00:03:27;04 --> 00:03:30;03
Calculus triangles?
To help you figure out,

56
00:03:30;04 --> 00:03:34;14
OK from one point to the
next just how much did Y

57
00:03:34;15 --> 00:03:37;06
Change? Just how much did X
change to go get your

58
00:03:37;07 --> 00:03:42;14
Rate of change. That,
OK? You can, again, do

59
00:03:42;15 --> 00:03:45;01
whatever you want, you
can look at your points

60
00:03:45;02 --> 00:03:48;13
to ask yourself the question
how much did Y change

61
00:03:48;14 --> 00:03:53;08
How much did X change
and go from there. You can

62
00:03:53;09 --> 00:03:56;14
Look at your graph and do
little calculus triangles

63
00:03:56;15 --> 00:04:00;10
To keep track of how much
did Y change, how much

64
00;04:00;10 --> 00:04:03;14
Did X change, get your
rate of change from there.

65
00:04:03;15 --> 00:04:06;13
Again, we did a few
different ways of this back

66
00:04:06;14 --> 00:04:09;10
In the day, and it's coming
back. It's back to haunt you.

67
00:04:09;11 --> 00:04:14;08
There you go. Here's the
thing- I'll let you guys figure

68
00:04:14;09 --> 00:04:16;03
Out the rate of change
because I want you guys to

69
00:04:16;04 --> 00:04:18;09
Have practice with this, but
when you come down to

70
00:04:18;10 --> 00:04:21;02
the next series, what
points are you

71
00:04:21;03 --> 00:04:23;29
going to change between
on this next column?

72
00:04:24;00 --> 00:04:25;07
[Negative 3 negative 2]

73
00:04:25;08 --> 00:04:28;06
Good, you're going to pick
up where you left off. Pick

74
00:04:28;07 --> 00:04:33;05
Up at negative 3, and
go to the next interval

75
00:04:33;06 --> 00:04:35;02
Which would be at

76
00:04:35;03 --> 00:04:35;13
[2]

77
00:04:36;04 --> 00:04:38;02
Negative 2. Because,
again, you're doing interval

78
00:04:38;03 --> 00:04:42;07
Size 1 on this particular thing.
Do this all the way

79
00:04:42;08 --> 00:04:47;04
From negative 4 to positive
4. We'll regroup in a

80
00:04:47;05 --> 00:04:49;06
Moment. Mark, set, go. Pop
each other, work together,

81
00:04:49;07 --> 00:04:51;06
Agree with each other,
debate with each other,

82
00:05:51;07 --> 00:04:53;05
All that good stuff.