extrema - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Optimization : extrema

extrema

find relative extrema of an expression

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

extrema(expr, constraints)

extrema(expr, constraints, vars)

extrema(expr, constraints, vars, 's')

Parameters

expr

-

expression whose extrema are to be found

constraints

-

constraint or set of constraints

vars

-

variable or set of variables

s

-

unevaluated name

Description

• 

The extrema function can be used to find extreme values of a multivariate expression with zero or more constraints. Candidates for extreme value points can also be returned. The extrema are returned as a set, and the candidates are returned as a set of sets of equations in the appropriate variables.

• 

expr must be an algebraic expression. The constraints may be specified as either expressions or equations. When a constraint is given as an expression, it is understood that constraint = 0. If no constraints are to be given, then the empty set {} is used in the parameter list. If vars is not given then all name indeterminates in the expr and constraints are used. vars must be specified if the fourth parameter s is given. The candidates for the extreme value points are returned in s.

• 

When the candidates cannot be expressed in closed form, s will contain the system of equations which when solved will produce these candidates.

• 

This function employs the method of Lagrange multipliers.

Examples

extremaax2+bx+c,,x

144acb2a

(1)

extremaaxyz,x2+y2+z2=1,x,y,z

max0,193a,193a,min0,193a,193a

(2)

fx2+y212z;g1x2+y216;g2x+y+z=10

f:=x2+y2z

g1:=x2+y216

g2:=x+y+z=10

(3)

extremaf,g1,g2,x,y,z,'s'

642,6+42

(4)

s

x=22,y=22,z=42+10,x=22,y=22,z=42+10

(5)

See Also

maximize

minimize

 


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam