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Problem 30 Use Theorem 2 below to find the local extrema of f x y...

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Calculus

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Problem 30 Use Theorem 2 below to find the local extrema of f x y 2y 6xy x Theorem 2 If 1 z f x y 2 f a b 0 and fy a b 0 3 All second order partial derivatives of exist in some circular region containing a b as center 4 Afrz a b B fay a b C f a b Then Case 1 If AC B 0 and A 0 then f a b is a local maximum Case 2 If AC B 0 and A 0 then f a b is a local minimum Case 3 If AC B 0 then f has a saddle point at a b Case 4 If AC B 0 the test fails

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