Engineering Calculus Notes 346

Engineering Calculus Notes 346 - ı 2 y −→ 2 z −→ k...

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334 CHAPTER 3. REAL-VALUED FUNCTIONS: DIFFERENTIATION We begin by looking for the Critical Points of f : ∂f ∂x = 4 x ∂f ∂y = 2 y ∂f ∂z = 2 y all vanish only at the origin, and f (0 , 0 , 0) = 0 . as to Boundary Behavior : −→ f ( x,y,z ) = 4 x −→ ı + 2 y −→ 2 z −→ k −→ g ( x,y,z ) = 2 x −→
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Unformatted text preview: ı + 2 y −→ + 2 z −→ k and the Lagrange Multiplier Equations read 4 x = 2 λx 2 y = 2 λy − 2 z = 2 λz. The Frst equation tells us that either λ = 2 or x = 0; the second says that either λ = 1 or y = 0...
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