Classify the critical points of f(x,y)= 4+x^3 + y^3 -3xy
"f_x=3x^2-3y"
"f_y=3y^2-3x"
Find the critical point(s)
Then
"y=x^2"
"x^4-x=0"
Critical points are "(0, 0), (1, 1)"
"f_{xy}=f_{yx}=-3"
"f_{yy}=6y"
Point "(0,0)"
Then "f(0,0)" is not a local maximum or minimum. Point "(0,0)" is a saddle point of "f."
Point "(1,1)"
"D(1,1)=36(1)(1)-9=27>0""f_{xx}(1,1)=6(1)=6>0"
Then "f(1,1)=3" is a local minimum.
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