In using Lagrange multipliers to minimize the function $f ( x , y ) = x ^ { 2 } + y ^ { 2 }$ subject to the constraint that $x y = 2$ , what is the value of the multiplier $\lambda$ ?
A) $\frac { 1 } { 2 }$
B)1
C) $\frac { 3 } { 2 }$
D)2
E)
$\frac { 5 } { 2 }$
F)3
G) $\frac { 7 } { 2 }$
H)4

Question

In using Lagrange multipliers to minimize the function $f ( x , y ) = x ^ { 2 } + y ^ { 2 }$ subject to the constraint that $x y = 2$ , what is the value of the multiplier $\lambda$ ?
A) $\frac { 1 } { 2 }$ 
B)1
C) $\frac { 3 } { 2 }$
D)2
E)
$\frac { 5 } { 2 }$
F)3
G) $\frac { 7 } { 2 }$ 
H)4

Quizplus · Accepted Answer

The Lagrange multiplier $\lambda$ is found by solving the system of equations derived from the gradients of the function and the constraint. Solving these equations gives $\lambda = 2$.

In Using Lagrange Multipliers to Minimize the Function f(x,y)=x2+y2f ( x , y ) = x ^ { 2 } + y ^ { 2 }f(x,y)=x2+y2

In Using Lagrange Multipliers to Minimize the Function $f ( x , y ) = x ^ { 2 } + y ^ { 2 }$