Calculates the local minimum of a function.

fMin(*f*(*var*),*var*,*lo*,*hi*[,*tol*])

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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.

# Related Commands

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