Secant Lines and Tangents
Play with this applet. You can use the given function or type in another one of your own choosing. You also get to pick the "step size" of h and see what happens to the slope of the secant line as it approaches the tangent line. Try changing the "step size" of h and see how this affects the estimate of the slope of the tangent line by clicking on the [+] or [-] buttons. At some point you will see that the secant slope is undefined. Can you explain why this happens?