The FalsePosition command numerically approximates the roots of an algebraic function, f, using a technique similar to the Secant method, but bracketing is incorporated.

Given an expression f and an initial approximate a, the FalsePosition command computes a sequence , =, of approximations to a root of f, where  is the number of iterations taken to reach a stopping criterion.

The FalsePosition command is a shortcut for calling the Roots command with the method=falseposition option.

functionoptions = list

A list of options for the plot of the expression f. By default, f is plotted as a solid red line.

lineoptions = list

A list of options for the lines on the plot. By default the lines are solid blue.

maxiterations = posint

The maximum number of iterations to to perform when numerically approximating a root of f. The default value of maxiterations depends on which type of output is chosen:

output=value : default maxiterations = 100

output=sequence : default maxiterations = 10

output=information : default maxiterations = 10

output=plot : default maxiterations = 5

output=animation : default maxiterations = 10

output = value, sequence, plot, animation, information

The return value of the function. The default is value.

output=value returns the final numerical approximation of the root.

output=sequence returns an expression sequence, , =, where the first  elements are the subintervals that contain an approximation and the  element is the final approximate root.

output=plot returns a plot of f with each iterative approximation shown and the relevant information about the numerical approximation displayed in the caption of the plot.

output=animation returns an animation of the numerical approximation on the plot of f.

output=information returns detailed information about the iterative approximations of the root of f.

pointoptions = list

A list of options for the points on the plot. By default, the points are plotted as green circles.

showfunction = true or false

Whether to display f on the plot or not.  By default, this option is set to true.

showlines = true or false

Whether to display lines that accentuate each approximate iteration when output=plot. By default, this option is set to true. To control the vertical lines, see the showverticallines and verticallineoptions options.

showpoints = true or false

Whether to display the points at each approximate iteration on the plot when output=plot. By default, this option is set to true.

showverticallines = true or false

Whether to display the vertical lines at each iterative approximation on the plot when output=plot. By default, this option is set to true.

stoppingcriterion = relative, absolute, function_value

The criterion that the approximation must meet before discontinuing the iterations. The following describes each criterion:

relative :  < tolerance

absolute :  < tolerance

function_value :  < tolerance

By default, stoppingcriterion=relative.

tickmarks = list

The tickmarks when output=plot or output=animation. By default, tickmarks are placed at the initial and final approximations with the labels a and b for the two initial approximates and the label  for the final approximation, where  is the total number of iterations used to reach the final approximation.  If the stopping criterion is not met, no tickmark will be placed on the last approximation. See plot/tickmarks for more detail on specifying tickmarks.

caption = string

A caption for the plot. The default caption contains general information concerning the approximation. For more information about specifying a caption, see plot/typesetting.

tolerance = positive

The error tolerance of the approximation. The default value is .

verticallineoptions = list

A list of options for the vertical lines on the plot. By default, the lines are dashed and blue.

view = [realcons..realcons, realcons..realcons]

The plot view of the plot when output = plot.  See plot/options for more information.