Property	Value
Hex Value	`$27`
Categories	Catalog > F Math > Math
Localizations	FR: `fMin(`

`fMin(`

Overview

Returns the value of variable where the local minimum of expression occurs, between lower and upper, with specified tolerance.

Availability: Token available everywhere.

Syntax

fMin(expression,variable,lower,upper[,tolerance])

Arguments

Name	Type	Optional
expression	expression
variable
lower
upper
tolerance		Yes

Location

math, MATH, 6:fMin(

Description

fMin(f(var),var,lo,hi[,tol]) finds the value of var between lo and hi at which the minimum of f(var) occurs. tol controls the accuracy of the minimum value computed. The default value of tol is 10^-5.

fMin( only works for real numbers and expressions. Brent's method for optimization is used for approximating the minimum value.

fMin(cos(sin(X)+Xcos(X)),X,0,2)
        1.076873875

Keep in mind that the result is the value of var, and not the value of f(var). In this example, 1.076873875 is not the lowest possible value of cos(sin(X)+Xcos(X)), but rather the X-value at which cos(sin(X)+Xcos(X)) is the lowest.

Advanced Uses

fMin( is sometimes useful in finding so-called "multiple roots" of a function. If the graph of your function appears "flat" near the root, fMin( might be able to find the value of the root more accurately than solve(.

Error Conditions

ERR:BOUND is thrown if the lower bound is greater than the upper bound.
ERR:DOMAIN is thrown if tol is 0.
ERR:TOL NOT MET is thrown if the tolerance is too small for this specific function.

Source: parts of this page were written by the following TI|BD contributors: alexrudd, burr, DarkerLine, GoVegan, kg583, thornahawk.

History

Calculator	OS Version	Description
TI-82	1.0	Added

Authors: Adrien Bertrand

fMin(