Finding the derivative at a point turns into a viewing window problem.[br]I want to find a delta-epsilon window so that the curve looks like a line.[br](I should not be able to tell the difference between the curve and the secant line from [br](c,f(c)) to (c+delta, f(c+delta)).)[br][br]I then approximate the derivative by finding rise/run for the line.

For most functions, it is easiest to use the calculator definition of derivative. Set x-scale to 0.001, and set y-scale to something that keeps the curve in the viewing window. [br][br]Use this method to find the derivative of the given function at three points. then try with another function.[br][br]If you look at a badly behaved function, like [math]f\left(x\right)=sin\left(\frac{pi}{x}\right)[/math] at x=4/101, you need a smaller epsilon.[br][br]This applet is meant as an illustration of the definition of a derivative at a point.[br][br]It has the advantage of showing that numeric differentiation is quite robust.[br]The default curve is a parabola, where students will be able to find the derivative symbolically.[br][br]