Let's say my function looks something like that. So this point right over here, the x-value is a, and the y-value is f of a. F of a, this point right over here, the x-value is b, and the y-value, of course, is f of b. F of b. F of b. So all the mean value theorem tells us is if we take the average rate of change over the interval, that at some point, the instantaneous rate of change, at least at some point in this open interval, the instantaneous change is going to be the same as the average change. Now what does that mean visually? So let's calculate the average change. The average change between point a and point b, well that's going to be the slope of the secant line. That's going to be the slope of the secant line.