00:04
Here we're looking to find the average rate of change for a function.
00:12
So let's remind ourselves what the average rate of change is.
00:15
The average rate of change is equal to the slope of the secant line.
00:23
The secant line is that line that connects two points on a curve.
00:28
So let's say we have this is our curve.
00:31
And we want to connect, we want to find the average rate of change between two different points.
00:38
This would be our first point.
00:41
So we might call that theta 1.
00:44
And this right here is our second point.
00:48
That's theta 2.
00:49
The average rate of change is going to be the slope of the secant line, which is the line that connects those two points.
00:57
It's a straight line.
00:59
So if you want to find the slope, remember slope equals the rise over the run.
01:13
So for this problem, the rise is going to be the change in the function's value.
01:22
So this value is r of theta 2.
01:26
That's the y coordinate of this dot right here.
01:29
And here, the y coordinate of this dot right here is going to be r of theta 1.
01:41
The rise is going to be the difference between those two y values.
01:46
So the rise is going to equal r of theta 2 minus r of theta 1.
02:04
And the run is going to be the difference between the x coordinates of those two points.
02:19
That's going to be our run...