0:00
Hi there.
00:01
So in this problem we are asked to estimate both the marginal cost and the marginal revenue for all these q values between 0 and 7.
00:12
So let's start with marginal costs.
00:15
So in order to estimate all of our marginal costs, we'll simply treat all these points on the table as if they're points on a graph and find the slope between them.
00:28
Okay? so let's start with zero.
00:33
So we're going to add.
00:37
Estimate marginal cost at zero now all we have we have zero and the only point next to zero is when q equals one so all we can do is treat these two as points and find the slope between them since derivative is roughly the same as slope in this context so the way we'll do all of these if we treat these as points in zero comma nine and one comma ten the slope would be we would do 10 minus nine on top and one minus zero on bottom.
01:13
Hopefully you can see that's just the same as the slope formula we know.
01:16
And we get one on top, one on bottom.
01:21
So we'll say one.
01:24
So we'll estimate c prime and zero to be one.
01:28
Okay.
01:31
Now let's look q equal one.
01:35
Again, there's several ways we could do this.
01:40
For q equals one, let's actually look on either side.
01:42
That'll give us a little better estimate of what the slope is.
01:45
So what we'll do, we'll connect the points to the left.
01:47
And to the right of one and it should give us a decent approximation.
01:56
Again, there's other ways we could do it.
01:58
We can do it in several different ways.
02:01
Well, let's choose that.
02:02
So we've got 2.
02:06
I'm sorry, we've got 12 is our c of 2 minus 9 was our c of 0.
02:15
We've got 2 minus 0.
02:17
That gives us 3 over 2.
02:19
About one and a half and we'll just keep doing this now down the line so you can probably see how this is going to go these we're just finding the average rates of change next time now between if we're centered at two let's go between one and three so the cue of three was 15 q of one was 10 and we had plugged in three and one for our inputs so we get five over two so this time we're about two and a half okay, we can just keep doing this.
02:55
C prime of 3.
02:57
We'll estimate if we're centered on 3, we're going between 2 and 4.
03:00
So we've got 19 minus 12 on top, 4 minus 2 on bottom.
03:07
We're getting 7 over 2, which is 3 .5.
03:11
So so far we're sensing a pattern.
03:13
We'll see if it holds up.
03:16
C prime of 4.
03:17
So let's go between 3 and 5.
03:21
24 minus 15.
03:25
And we had 5 minus 3 on bottom...
