00:01
So in this question, we're told that a cost function, it's given by capital c of x, it equals 5x squared plus 2.
00:12
And part a, we want to find the marginal cost, which is just the derivative of cost.
00:18
So that's going to be 10x.
00:22
We also want to find the derivative of the average cost.
00:26
So first of all, average cost, i'll just say, i'll call it a of x.
00:30
It's your cost function divided by x.
00:34
And so that's 5x plus 2 over x.
00:42
So the derivative of the average cost is 8 prime.
00:47
It's the derivative.
00:49
So it's going to be 5 plus.
00:51
So the derivative of 1 over x is negative 1 over x squared.
00:56
So really what we have is minus 2 over x squared.
01:04
So here's a marginal cost.
01:06
Here's the derivative of x squared...