00:01
So we want to determine where our rate is going to be maximized.
00:06
So in order to determine when something is going to be maximized, in this case, r of x, what we do is we take the derivative and we set that equal to zero.
00:16
And that can lead to two possibilities.
00:18
It can lead to basically a case where we have it crossing the graph here or we have a crossing the graph like this.
00:27
If it crosses the graph like this, we see that we will.
00:31
Were going from positive to negative, meaning we had a positive slope, we reached zero slope, and then we went to a negative slope.
00:38
So that means that this is a maximum, so we can maximize something.
00:42
Or in this case, we see that the slope was negative and then turned positive.
00:48
So a negative slope reaches that point and then turns positive.
00:52
Well, this is going to be a relative minimum.
00:54
So let's figure out how we can maximize r of x.
00:58
So r of x equals 2x times 4.
01:03
Minus x.
01:05
And i would advise that we start by multiplying this out.
01:10
So that's going to be 8x minus 2x squared.
01:15
So now when we take the derivative with respect to x or r prime of x, we get 8 minus 4x...