TI-BASIC:Fmin
Command Summary
Calculates the local minimum of a function.
Command Syntax
fMin(f(var),var,lo,hi[,tol])
Menu Location
While editing a program, press:
- MATH to open the Math menu
- 6 or use arrow keys to select
TI-83/84/+/SE
1 byte
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.