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Critical Points (Local Maximum, Local Minimum, Saddle Points)

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(a) Find all the critical points of f = xy + yz - zx + xyz (Hint: set f = 0)
(b) Classify the critical point of f as local maximum, local minimum or saddle points.

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The solution determines the critical points with details provided.

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Q (a) Find all the critical points of f = xy + yz - zx + xyz (Hint: set f '= 0)
Grad f = i(y -z + yz) + j(x + z + xz) + k(y - x + xy) = 0
Therefore,
y - z + yz = 0...(i)
x + z ...

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