00:01
We're given the following cost function and asked to minimize the average cost.
00:05
So first we need to say what is the average cost.
00:08
The average cost we put with c bar and we put it over the number of items which we say is x.
00:13
But i'm going to write this because i know we're taking the derivative.
00:16
I'd rather use the product rule.
00:18
I'm going to write that as 500 x to the negative 1 0 .02 x plus 2 cubed.
00:25
Now let's take the derivative of that c bar.
00:28
We're going to have the first and here's the second.
00:32
So we're going to take the first 500 x to the negative 1 times the derivative of the second which is going to be 3 0 .02 x plus 2 squared.
00:42
We have to take the derivative of what's inside.
00:45
So we need that 0 .02.
00:47
Now we're going to say plus, let me make sure i have enough parentheses there.
00:51
I think i do now, plus the second which is going to be 0 .02 x plus 2 cubed times the derivative of the first.
01:02
That's going to be negative 500 x to the negative 2.
01:06
Now i'm going to clean this up.
01:07
I'm going to get it in factored form because i know we need to have it set equal to 0.
01:11
So our greatest common factor here, we're going to have a parentheses.
01:15
Notice that both terms have a parentheses.
01:18
Both have a 500 and then both have, i'm going to change colors, this x and x.
01:25
So let's see what they have in common.
01:26
First of all, let's look at the parentheses.
01:28
They have two parentheses in common.
01:33
So that'll be a squared.
01:35
We have that 500 in common.
01:37
So i'm going to put that here.
01:38
Now for the x's, we pick the lowest exponent.
01:41
That's going to be x to the negative 2.
01:43
Now when we factor that, let's see what happens.
01:46
We don't, in the first term, we don't have the 500.
01:48
We don't have the parentheses...