Critical Points and the Second Derivative Test - Maple Help

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Critical Points and the Second Derivative Test

Description

Determine and classify the critical points of a multivariate function.

 

Critical Points and the Second Derivative Test

Objective Function f

x2+3 x y25 y3

x2+3xy25y3

(1)

List of Independent Variables

vx,y

v:=x,y

(2)

Equations f=0

 convertStudentMultivariateCalculusGradient,,list;

2x+3y2,6xy15y2

(3)

Critical Points

 tempremovehas,solve,v,Explicit,I:convertseqevalv,tempk,k=1..nopstemp,list

0,0,256,53

(4)

Second Derivative Test

StudentMultivariateCalculusSecondDerivativeTest,v=;

LocalMin=,LocalMax=,Saddle=256,53

(5)

Hessians and their Eigenvalues

TempStudentMultivariateCalculusSecondDerivativeTest,v=,output=hessian: for k to nopsTemp do Tempk,convertLinearAlgebraEigenvaluesTempk,list; end do; 

2000,0,2

2101025,272+12929,27212929

(6)

Commands Used

LinearAlgebra[Eigenvalues]

Student[MultivariateCalculus][Gradient]

Student[MultivariateCalculus][SecondDerivativeTest]

Related Task Templates

Multivariate Calculus > Derivatives > Expression

Calculus > Find Special Points on a Function

See Also

convert, critical points , Hessian , Student[MultivariateCalculus]


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