# 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.