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 checkbox toggles display of the tangent line, in red, and a readout, also in red, of the value of 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 Δx ; a yellow diamond on the graph mark (x + Δx, f(x+Δx)) and is related to the Δx slider position by a ghosted strut; and the value of Δy/Δx 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