The Definition of the Derivative

Use this applet to explore how the definition of the derivative relates to the secant and tangent lines at a point (a, f(a)). The red slider controls the location of the point (a,f(a)). The blue slider controls the value of "h" that determines the separation of the two points used for the secant line. Watch what happens to the secant line as you decrease the value of h. Pay specific attention to the slope in the equation of the secant line shown at the bottom. What happens to the secant line when h = 0? Why? Now turn on the tangent line to see how it compares to the secant line.