Evaluate numerically:

Evaluate to high precision:

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

Evaluate efficiently at high precision:

The maximum of all elements of a matrix:

The maxima of all rows:

The maxima of all columns:

For Interval objects, Max gives the maximum element in all intervals:

For CenteredInterval objects, Max[Δ₁,Δ₂] gives an interval containing Max[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 Max function using MatrixFunction:

Values of Max at fixed points:

Values at infinity:

Evaluate symbolically:

Solve equations and inequalities:

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

Plot the Max of several functions:

Plot Max in three dimensions:

Plot Max of two functions in three dimensions:

Max is only defined for real-valued inputs:

The range of Max is all real numbers:

Max effectively flattens out all lists:

Basic symbolic simplification is done automatically:

Additional simplification can be done using Simplify:

Multi-argument Max is generally not an analytic function:

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

Max can have any monotonicity depending on its arguments:

is not surjective:

Max 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 max of a list:

Use on some different types of data:

Create a function that computes the max 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 max of non-negative functions will be another non-negative function. Use that to generate interesting positive functions. These are all non-negative functions:

The max will also be non-negative:

Here is another example:

The max of increasing functions will be another increasing function. Use that to generate interesting increasing functions:

The max of convex functions will be another convex function. Use that to generate interesting convex 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: