Secant Lines and Tangents

We talked some more today about how to find derivatives and exactly what the definition of a derivative is.

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?