- secant tangent applet Move the green dot toward the red one to see the secant line become the tangent. Pull down the menu above the graph for more provocative examples, or enter your own function, e.g. abs(x). Read the directions for how to zoom in, etc.
- function, derivative, integral Click the Show Derivative box (ignore the integral for now; we'll get to it later). Then click and hold down on the graph, move it, and see the derivative change. To start again hit the browser Reload or Refresh button.
- derivative puzzles When you're comfortable with getting the general shape of the derivative function from looking at the graph of the original function, play this derivative puzzle game that asks you to match function graphs with those of their derivatives.
- surfing for derivatives A neat way to visualize the derivative.
- derivatives of exponentials Shows f(x)=b^x and its derivative for different values of b.
- linear approximation
- epsilon-delta applet You can read the instructions above the applet shown, then try it out. Then go down below it and hit the Launch EpsilonDelta button. That configuration of the applet has some examples in the pull-down menu that are well worth thinking about.
- falling cantaloupe movie This is just what it sounds like.
- Newton's method applet
- another Newton's method applet This one does one step at a time.
- another Newton's method applet This one lets you enter your own function.
- Two examples of weird behavior: http://www.dougshaw.com/sesem/Summer14.html and http://www.dougshaw.com/sesem/Summer15.html
- Newton's method fractal applet If you use Newton's method on complex polynomials, you get a fractal.
- another Newton's method fractal applet The picture is smaller, but you can choose where to zoom in.
- get right-hand and left-hand estimates simultaneously (plus others)
- some interesting examples
- use sliders