Suppose the Partial Derivatives of a Lagrange Function F(x, Y $\frac { \partial F } { \partial x }$

question 114

Multiple Choice

Suppose the partial derivatives of a Lagrange function F(x, y, λ) are $\frac { \partial F } { \partial x }$ = 2 - 8λx, $\frac { \partial \mathrm { F } } { \partial \mathrm { y } }$ = 1 -2λy, $\frac { \partial F } { \partial \lambda } = 32 - 4 x ^ { 2 } - y ^ { 2 }$ What values of x and y minimize F(x, y, λ) ? (Assume x and y are positive.)

• A) (4, 2)
• B) (2, 4)
• C) (2 \(\sqrt { 2 }\) , \(\sqrt { 4 }\) )
• D) (2, \(\sqrt { 2 }\) )
• E) none of these

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