The [color=#0000ff]blue line[/color] represents the [color=#0000ff]secant[/color] between 2 points.[br]The [color=#ff0000]red line[/color] is the [color=#ff0000]tangent[/color] at the point on the curve.[br][br]The horizontal distance between the two points is given by [math]h[/math]. [br][br]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]What do you notice as you reduce the distance between the 2 points? [br][br]

What is the gradient of the secant joining [math](a,f(a))[/math] and [math](b,f(b))[/math]? [br][br]Move the slider to make the distance [math]h[/math] become smaller. [br][br]What do you notice about the formula of the gradient of the secant? [br][br]What do you notice about the gradient of the secant?