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Find all points (x,y) where g(x,y)=1/3x^3+y^2+2xy-6x-3y+4 has a possible relative maximum, minimum, or saddle points. Then, use the second-derivative test to determine, if possible, the

Find all points (x,y) where g(x,y)=1/3x^3+y^2+2xy-6x-3y+4 has a possible relative maximum, minimum, or saddle points.

Then, use the second-derivative test to determine, if possible, the nature of f(x,y) at each of these points.

If the second-derivative test is inconclusive, state so.

(MAKE SURE TO INCLUDE ALL NECESSARY STEPS)

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