SECANT APPROXIMATION

Choose a value for $$x$$, then use the coordinate readout to calculate slopes of secant lines to a graph, or adjust the value of $$\Delta x$$ while the computer calculates and displays the secant. Observe that as $$\Delta x$$ decreases, the secant line gets closer to the tangent line.

A graphing window displays in cyan the graph of a function $$f(x)$$ which is chosen from a pull down menu below. A slider controls the value of $$x$$, and $$(x, f(x))$$ is marked on the graph with a red diamond, related to the $$x$$ slider by a ghosted red strut.

A checkbox toggles display of the tangent line, in red, and a readout, also in red, of the value of $$\frac{dy}{dx}$$ at the chosen value of $$x$$.

A second checkbox toggles display of several components, all colored yellow. A slider centered at the chosen value of $$x$$ controls the value of $$\Delta x$$ a yellow diamond on the graph mark $$(x + \Delta x, f(x + \Delta x))$$ and is related to the $$\Delta x$$ slider position by a ghosted strut; and the value of $$\frac{\Delta y}{\Delta x}$$ is read out below.

Rolling the mouse over the graphing window creates crosshairs and a readout of the values of $$x$$ and $$y$$. Depressing the mousekey suppresses this readout.

© 2010 H. Miller, H. Burgiel, and J.-M. Claus