Secant Approximation -- Help

 

Choose a value for x, then use the coordinate readout to calculate slopes of secant lines to a graph, or adjust the value of Δx while the computer calculates and displays the secant. Observe that as Δx 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 second slider controls the value of Δx . It is below the x slider, and moves so it is always centered at the current value of x. The point (x+Δx, f(x+Δx)) is marked on the graph with a yellow diamond, related to the Δx slider by a ghosted yellow strut. The secant line through the red diamond and the yellow diamond is drawn in yellow.

A checkbox toggles display of the tangent line, in red.

The value of Δy/Δ x is indicated in yellow, and if the tangent line is displayed the value of dy/dx is indicated in red.

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, Heidi Burgiel, and J.-M. Claus