0:00
All right.
00:01
So here's the problem.
00:02
We're given a marginal cost formula function.
00:06
We want to produce skateboards.
00:07
There's a marginal cost function of 180 minus 2x, and there's an initial fixed startup cost of $100.
00:15
We want to know what the cost is to produce 30 skateboards.
00:19
So if we produce just one, you know, our marginal cost is like 180 minus two, and then it's like 178.
00:30
Plus the $100 is like $278 if we produce one.
00:33
But as we produce more, it should be less per item, per unit, you know, mass producing things.
00:41
Okay.
00:43
So what you need to realize is the marginal cost is the change in the cost compared to the change in number of items you produce.
00:53
So it's change in cost over the change in the number of items.
01:00
Okay, so that function is our marginal cost.
01:05
That's the 180 minus 2x.
01:08
So if you multiply both sides by dx, we have dc.
01:12
The change in the cost is 180 minus 2x dx.
01:18
Okay, so what we're going to do now to find the cost, what the actual cost is, is we're going to integrate both of these sides.
01:31
So when we integrate the change in the cost or the derivative of the cost, we just get the cost function.
01:40
So the cost function, total cost function, is going to equal the antiderivative of our marginal cost function.
01:49
So that's going to be 180x minus 2x squared over 2.
01:58
The twos can reduce out, so it's just going to be x squared, so minus x squared.
02:07
Now, plus some constant.
02:09
I don't want to put c down, plus n for constant.
02:16
Okay, i need to see for cost...