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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.
  • 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.
  • xElementIntegers can be used to specify that a particular variable can take on only integer values.
EXAMPLESCLOSE ALL
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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