And so what's the slope of the secant line between these two points? It would be change in the vertical, which would be f of x minus f of a, over change in the horizontal, over x minus a. So let me do that in a purple color, over x minus a. Now, how can we get a better and better approximation for the slope of the tangent line here? Well, we could take the limit as x approaches a. As x gets closer and closer and closer to a, the secant line slope is going to better and better and better approximate the slope of the tangent line, this tangent line that I have in red here. So we would want to take the limit as x approaches a here.