00:01
Okay, so for this question, we are given the function f of x equals x.
00:07
Let me write that over here.
00:09
F of x equals x.
00:11
And we are asked to come up with some sort of expression to relate and find the average rate of change between two points.
00:23
One that starts at x, let's just label this x, and one that's at x plus h for this function.
00:33
So we're saying create an expression, let me actually type this because that might be easier.
00:48
If it'll let me type, which it won't, that's okay.
00:52
Create an expression to represent the average rate of change between x and x plus h.
01:20
Basically what this means is, so if we have a point x and we put it into our function, f of x equals x, we're going to get something out, right? we're going to get f of x, whatever that is.
01:38
Likewise, if we put x plus h into our function, we're going to get something out, f of x plus h, whatever that is.
01:50
That's basically the meaning of an x and a y value.
01:53
You can also think of this function as being y equals x.
01:57
So if we put an x value in, we're getting a y value out.
02:00
That's basically all we're saying.
02:04
So once we know that, we can think about what a rate of change means.
02:10
A rate of change is a slope, is another word you might have heard for that.
02:14
And it basically just means we're finding the difference in the y values divided by the difference in the x values...