This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

MaxValue

 MaxValuegives the maximum value of f with respect to x. MaxValuegives the maximum value of f with respect to x, y, .... MaxValuegives the maximum value of f subject to the constraints cons. MaxValuegives 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.
• Integers can be used to specify that a particular variable can take on only integer values.
Find the maximum value of a univariate function:
Find the maximum value of a multivariate function:
Find the maximum value of a function subject to constraints:
Find the maximum value as a function of parameters:
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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 Scope   (15)
Unconstrained univariate polynomial maximization:
Constrained univariate polynomial maximization:
Univariate transcendental maximization:
Univariate piecewise maximization:
Multivariate linear constrained maximization:
Linear-fractional constrained maximization:
Unconstrained polynomial maximization:
Constrained polynomial optimization can always be solved:
The maximum value may not be attained:
The objective function may be unbounded:
There may be no points satisfying the constraints:
Algebraic maximization:
Bounded transcendental maximization:
Piecewise maximization:
Unconstrained parametric maximization:
Constrained parametric maximization:
Integer linear programming:
Polynomial maximization over the integers:
 Options   (1)
Finding the exact maximum can take a long time:
With WorkingPrecision, you get an exact maximum value, but it might be incorrect:
 Applications   (3)
Find the maximal area among rectangles with a unit perimeter:
Find the maximal area among triangles with a unit perimeter:
Find the maximum height reached by a projectile:
Find the maximum range of a projectile:
Maximize gives both the value of the maximum and the maximizer point:
For strict polynomial inequality constraints MaxValue may be much faster than Maximize:
MaxValue gives an exact global maximum value of the objective function:
NMaxValue attempts to find a global maximum numerically, but may find a local maximum:
FindMaxValue finds local maxima depending on the starting point:
MaxValue can solve linear programming problems:
LinearProgramming can be used to solve the same problem given in matrix notation:
MaxValue requires that all functions present in the input be real-valued:
Values for which the equation is satisfied but the square roots are not real are disallowed:
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