SECANT APPROXIMATION

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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.
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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