The Secant Line Approaching The Tangent Line

Here is a Geometer's Sketchpad video with audio Links to an external site. (Larger Version Links to an external site.) of me describing approximating the slope of a tangent line with a secant line.

Here is a Winplot demonstration Links to an external site. of a secant line that can be used to approach a tangent line.  You may need to download the file to your desktop and then use the freeware Winplot Links to an external site. to open the file (by opening Winplot, clicking on Window, clicking on 2-dim, clicking on File, clicking on Open, and then opening SecantSlope from your desktop.  You can use the sliders to vary the values of A and H.  The A-value gives you the x-value at a point on the graph of the function you are looking at.  The H-value gives you the x-value of another point on the graph of the function you are looking at in terms of A + H (so H is your delta x).  The secant line through the points on the graph of the given function with x-values of A and A + H is graphed and its slope displayed at the top of the graph.  The default function is f(x) = 3sin(x), a function from trigonometry.  This function is named FN and you can edit the definition of FN by clicking on Equa, choosing User functions ... , highlighting the function and editing its definition.  Changing the definition to x^2 for example will produce a different graph.