00:01
This question, we're given the marginal cost of product is given by this.
00:04
The cdx is 16 over cube root of 16x plus 9.
00:10
We can rewrite it as 16 times 16x plus 9 to the power minus 1 3rd.
00:18
As cube root is power 1 3rd but i'm bringing the denominator up to the numerator so it's minus 1 3rd.
00:27
Now x is the number of units.
00:29
We're given when x is 17, c is 120, part a we want to find the cost function cx.
00:39
And that would be integrating the dcdx function with respect to x.
00:54
So cx is now 16 is constant.
01:01
It can be brought outside the integration.
01:03
So we're integrating 1 over cube root of 16x plus 9, which can be written as this part here.
01:17
Now in general, when i integrate a x plus b to the power and respect to x, it will be just repeat wireless in the bracket a x plus b.
01:32
Now add one to the power so there'll be n plus 1 divided by the new power and by the a next to the x.
01:45
So our cost function will be 16 times let's integrate this.
01:53
Where minus 1 third is our n, 16 is our a.
01:59
So we will have 16x plus 9 to the power minus 1 3rd and add 1 to the power, divide by the new power, and by 16.
02:14
For the plus d, where d is a constant...