00:01
So here we've got a math -heavy question.
00:02
We're told that total cost is 2 over 3 q cubed minus 10 q squared plus 200 q plus 50.
00:14
So a, right, here's the fixed cost, right? the fixed cost is simply equal to 50 because this is the part that doesn't vary with q, right? the other way you could think about it is put in q equal zero.
00:32
Fixed cost or whatever you have to pay if you shut down production.
00:35
So if you put in q equal zero, only the constant is left.
00:39
And that makes this part the variable cost, right? this is the variable cost because that's all the parts that do vary with q, right? so a, b, relatively straightforward.
00:54
Average variable cost is equal to variable cost divided by q.
01:00
So this will be 2 over 3 q squared minus 10 q plus 200, right? average fixed cost is fixed cost over q is 50 over q.
01:14
Average total cost is more of the same, right? it is total cost over q, which is just a total cost.
01:22
The sum of these two things, right? we're dividing the whole thing by q instead of doing it by parts.
01:30
So there would be average total cost.
01:32
Marginal cost is the one that's more interesting.
01:34
Marginal cost is the derivative of total cost with respect to quantity.
01:39
So now we need to differentiate, right? for the first one, the power three comes down...