The horizontal distance between the two points is given by [math]h[/math]. Use the slider to change the value of [math]h[/math]. Decreasing the value of [math]h[/math] will bring the two points closer together.[br][br]You will notice as [math]h[/math] decreases and approaches zero, the line between the two points approaches the tangent of the curve at [math]x[/math].[br][br]Therefore we can say that as [math]h\longrightarrow0[/math], the gradient of the secant will approach the gradient of the function at [math]x[/math].