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Find and Classify All Critical Points of F(x,y,z) = X3

Question 36

Multiple Choice

Find and classify all critical points of f(x,y,z) = x3 + xz2 + 3x2 + y2 + 2z2 - 9x - 2y -10.


A) local minimum at (-2, 1, 3) , (-2, 1, -3) , (-3, 1, 0) and saddle point at (1, 1, 0)
B) local minimum at (-2, 1, 3) , (-2, 1, -3) and local maximum at (-3, 1, 0) , (1, 1, 0)
C) local minimum at (1, 1, 0 ) and saddle point at (-2, 1, 3) , (-2, 1, -3) , (-3, 1, 0)
D) local maximum at (-2, 1, 3) , (-2, 1, -3) , (-3, 1, 0) and saddle point at (1, 1, 0)
E) local minimum at (-2, 1, 3) , (-3, 1, 0) , local maximum at (1, 1, 0) , and saddle point at (-2, 1, -3)

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