Suppose we want to maximize the function f(x, y, z)= xyz with respect to the constraint equation x² + y²+z²=3. Which of the following equations is NOT part of the system of equations that we set up by the method of Lagrange multipliers? (a) yz = 12x. (b) xz = λ2y. (c) xy my = 2z. (d) x² + y² + z² = 4. (e) They are all part of the system.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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4. Suppose we want to maximize the function f (x, y, z) = xyz with respect to the
constraint equation x² + y²+z²=3. Which of the following equations is NOT part
of the system of equations that we set up by the method of Lagrange multipliers?
(a) yz = 12x.
(b) xz = 12y.
(c) xy = 1.2z. (d) x² + y² + z² = 4.
(e) They are all part of the system.
5. Referring to question 4, which of the following points is NOT a critical point found
by the method of Lagrange multipliers?
(2) (0,0,0). (b) (1,1,1). (c) (-1,-1,-1). (d) (1,-1,1).
(e) None of the other choices, or more than one of the other choices.
Transcribed Image Text:4. Suppose we want to maximize the function f (x, y, z) = xyz with respect to the constraint equation x² + y²+z²=3. Which of the following equations is NOT part of the system of equations that we set up by the method of Lagrange multipliers? (a) yz = 12x. (b) xz = 12y. (c) xy = 1.2z. (d) x² + y² + z² = 4. (e) They are all part of the system. 5. Referring to question 4, which of the following points is NOT a critical point found by the method of Lagrange multipliers? (2) (0,0,0). (b) (1,1,1). (c) (-1,-1,-1). (d) (1,-1,1). (e) None of the other choices, or more than one of the other choices.
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