# Min Command

From GeoGebra Manual

- Min( <List> )
- Returns the minimum of the numbers within the list.
**Example:**`Min({-2, 12, -23, 17, 15})`

yields*-23*.

**Note:**If the input consists of non-numeric objects, then this command considers the numbers associated with those objects. If you have a list of segments for example, the command Min( <List> ) will yield the minimum segment length.- Min( <Interval> )
- Returns the lower bound of the interval.
**Example:**`Min(2 < x < 3)`

yields*2*.

**Note:**Open and closed intervals are not distinguished.- Min( <Number>, <Number> )
- Returns the minimum of the two given numbers.
**Example:**`Min(12, 15)`

yields*12*.

- Min( <Function>, <Start x-Value>, <End x-Value> )
- Calculates (numerically) the
**local**minimum point for function in the given interval. Function should be continuous and have only one*local*minimum point in the interval (and no local maximum). **Note:**For polynomials you should use the Extremum Command.**Example:**`Min(exp(x) x^3,-4,-2)`

creates the point (-3, -1.34425) .

- Min( <List of Data>, <List of Frequencies> )
- Returns the minimum of the list of data with corresponding frequencies.
**Example:**`Min({1, 2, 3, 4, 5}, {0, 3, 4, 2, 3})`

yields 2, the lowest number of the first list whose frequency is greater than 0.

**Note:**

- If you want the minimum of two functions
`f(x)`

and`g(x)`

then you can define`(f(x) + g(x) - abs(f(x) - g(x)))/2`

- See also Max Command, Extremum Command and Function Inspector Tool.

## CAS Syntax

- Min( <Function>, <Start x-Value>, <End x-Value> )
- Unlike in the Algebra View, this syntax will give the minimum over the interval, including endpoints
**Example:**`Min(x^2,-1,2)`

yields the point*(0,0)*`Min(-x^2,-1,2)`

yields the point*(2,-4)*