BUILT-IN MATHEMATICA SYMBOL

# MaxValue

MaxValue[f, x]
gives the maximum value of f with respect to x.

MaxValue[f, {x, y, ...}]
gives the maximum value of f with respect to x, y, ....

MaxValue[{f, cons}, {x, y, ...}]
gives the maximum value of f subject to the constraints cons.

MaxValue[{f, cons}, {x, y, ...}, dom]
gives the maximum value of f over the domain dom, typically Reals or Integers.

## Details and OptionsDetails and Options

• MaxValue[...] is effectively equivalent to First[Maximize[...]].
• MaxValue gives the supremum of values of f. It may not be attained for any values of x, y, ....
• cons can contain equations, inequalities or logical combinations of these.
• If f and cons are linear or polynomial, MaxValue will always find a global maximum.
• MaxValue will return exact results if given exact input.
• If MaxValue is given an expression containing approximate numbers, it automatically calls NMaxValue.
• If no domain is specified, all variables are assumed to be real.
• can be used to specify that a particular variable can take on only integer values.
• If the constraints cannot be satisfied, MaxValue returns .

## ExamplesExamplesopen allclose all

### Basic Examples (4)Basic Examples (4)

Find the maximum value of a univariate function:

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Find the maximum value of a multivariate function:

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Find the maximum value of a function subject to constraints:

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Find the maximum value as a function of parameters:

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