Given the equation z = x^2 + y^3 + xy, find the critical points of the equation and identify wether they are mins maxes or neither. I got the points (0,0,0) neither, (-1/12, 1/6, -1/432) neither. Is this right?

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Given the equation z = x^2 + y^3 + xy, find the critical points of the equation and identify wether they are mins maxes or neither. I got the points (0,0,0) neither, (-1/12, 1/6, -1/432) neither. Is this right?

MIT 18.02 Multivariable Calculus, Fall 2007
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z=f(x,y) f(x,y) = x^2+y^3+xy Then find the first partial derivatives (fx) and (fy) fx= 2x+y=0 ,fy=3y^2+x=0 The critical points are (0,0) and (-1/12,1/6) Using the second derivative test (0,0) is a saddle point While (-1/12,1/6) is a minimum

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