00:01
So to find the instantaneous revenue, what we need to do is take a limit, and that limit should remind you much of the tangent slopes that we've been calculating.
00:10
So we'll take the limit as some h goes to zero of our revenue at c plus h, c being the place of interest that we're interested in, the number of computers in this case, minus r of c all divided by h.
00:24
So let's do this for any c, and then we can plug in the values of c that we're interested.
00:28
So we'll have the limit as h approach to zero.
00:32
Let's plug in c plus h into our function.
00:35
So we'll have 0 .4 times c plus h minus 0 .001 c plus h all squared.
00:43
Now plug c into our function.
00:45
That's 0 .4c minus 0 .001c squared, all divided by h.
00:55
Now let's expand.
00:57
We'll have 0 .4c plus 0 .4h by distribution.
01:00
We'll have minus 0 .001 c squared, minus 0 .002 ch, that's 2ch multiplied by that coefficient, and then we'll have minus 0 .001h squared.
01:16
Those are the three terms we get from squaring c plus h.
01:19
We'll then need to subtract these two terms, and note the signs change by distribution.
01:27
Now let's see, are there any like terms? those without h in them should cancel.
01:31
So we see that this with that and h cancels away...