Evaluate numerically:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

Evaluate efficiently at high precision:

The minimum of all elements of a matrix:

The minima of all rows:

The minima of all columns:

For Interval objects, Min gives the minimum element in all intervals:

For CenteredInterval objects, Min[Δ₁,Δ₂] gives an interval containing Min[a₁,a₂] for any a_i∈Δ_i:

Compute average-case statistical intervals using Around:

Compute the elementwise values of an array using automatic threading:

Or compute the matrix Min function using MatrixFunction:

Values of Min at fixed points:

Values at infinity:

Evaluate symbolically:

Solve equations and inequalities:

Find a value of x for which Min[{Sin[x],Cos[x]}]1/2:

Plot the Min of several functions:

Plot Min in three dimensions:

Plot Min of three functions in three dimensions:

Min is only defined for real-valued inputs:

The range of Min is all real numbers:

Min effectively flattens out all lists:

Basic symbolic simplification is done automatically:

Additional simplification can be done using Simplify:

Multi-argument Min is generally not an analytic function:

It will have singularities where the arguments cross, but it will be continuous:

Min can have any monotonicity depending on its arguments:

is not surjective:

Min can have any sign depending on its arguments:

First derivative with respect to x:

Higher derivatives with respect to x:

Formula for the derivative with respect to x:

Compute the indefinite integral using Integrate:

Verify the anti-derivative:

Definite integrals:

Create a function that computes the cumulative min of a list:

Use on some different types of data:

Create a function that computes the min of a sequence given by a function:

Try it for some different sequences:

Create a function that gives the positive part and another that gives the negative part:

Here are some examples:

The min of non-positive functions will be another non-positive function. Use that to generate interesting negative functions. These are all non-positive functions:

The max will also be non-negative:

Here is another example:

The min of decreasing functions will be another decreasing function. Use that to generate interesting decreasing functions:

The min of concave functions will be another concave function. Use that to generate interesting concave functions:

Max and min can be used to model Boolean operations for implicit regions. The intersection is equivalent to and, similarly, the union is equivalent to .

Consider the following two regions:

This is their intersection done with either Boolean operations or max:

This is their union done with either Boolean operations or min: