00:01
In part a, we want to know if the integral of the marginal cost function can be used to find a fixed cost.
00:12
Well, the answer is no.
00:14
This is the variable cost.
00:17
If you go from 0 to a, that will be the variable cost of producing a unit.
00:34
So, no, not the fixed cost.
00:36
And then b, if the integral between 0 and 5 of f prime of t dt is 0, then f is constant on the interval from 0 to 5.
01:01
Well, that's not true either.
01:04
For example, f of t is equal to, oh, let's see, let's pick something.
01:18
2t minus, if f prime of t is 2t minus 5, then your integral from 0 to 5 of f prime t dt is equal to 2t squared over 2 minus 5t, evaluated between 5 and 0, so that is 5 squared, 25 minus 25, and then at 0, it is minus 0 minus 0.
02:00
So this is 0, but f of t, which is t squared minus 5t, is not constant on the interval from 0 to 5.
02:21
So there is an example to disprove that...