00:01
In this problem, we are given an expression for the cost function, and we want to find the value of the minimum average cost.
00:07
So first, let's define our average cost.
00:15
The average cost will be defined as c bar of x, which we find by taking our cost function and dividing it by x.
00:23
We obtain x squared plus 65 plus 432 divided by x.
00:35
Now to minimize this function, we want to calculate its first derivative.
00:40
So c bar prime will give us 2x minus 432 divided by x squared.
00:49
To find the critical point, we want to find the values of x for which c bar prime of x is equal to zero, and we see that this will be the case when x cubed is equal to 432 divided by 2.
01:15
In solving for x, we obtain x equal to 6.
01:19
This here is our critical point, and to make sure this critical point will in fact minimize our average cost, let's look at our second derivative.
01:31
Let's calculate c bar prime prime...