root

Format: root( f(x), x, x1, x2 )

Arguments: (real) f(x) Function or expression to be solved

(node) x Name of the input variable in f(x)

(real) x1 Initial guess for the value of x or lower limit on x

(real) x2 Optional upper limit on x

Returns: (real) The value of x where f(x) = 0

Description: Root finds the value of x such that f(x) = 0. You must supply root with either a single point guess for the value of x or a lower- and upper-limit. Toot uses different methods to find the value of x depending on which of these starting methods you provide. If you provide a value for both x1 and x2, the values f(x1) and f(x2) must be of different signs. If this condition is met, root will always find a solution. If you provide a value for x1 only, root will search for a solution by adjusting x1 down hill until it finds a solution or until a local minimum is encountered. If root fails to converge on a solution, try another value for x1.

Root is an approximated function and is subject to the tolerance set by precision. Root creates a temporary variable named x. If a node with this name already exists, it is replaced for all evaluations of f(x) and is then restored to its original state.

Note: If the expression f(x) is a tree node rather than a function based on x, the reset primitive must be used to cause the tree to recalculate on each iteration. Constants retain their value from the first evaluation and return this value on all subsequent evaluations. To cause the constant to be reevaluated, use an expression similar to

root({reset,f},x,x1,x2)

rather than

root(f,x,x1,x2))

Examples: root(x^2-25,x,0,10) = 5

f(x):=x/3-4

root(f(x),x,10) = 12

See Also: precision, solve, minimize