Find the extrema of
3x^2-y^2+x^3
"f_x=6x+3x^2"
"f_y=-2y"
Find the critical point(s)
"Point(-2,0), Point(0,0)"
"f_{xy}=0"
"f_{yy}=-2"
"D=\\begin{vmatrix}\n 6+6x & 0 \\\\\n 0 & -2\n\\end{vmatrix}=-12-12x"
"Point(-2,0)"
"D=-12-12(-2)=12>0"
Then "f(-2, 0)" is a local maximum.
"Point(0,0)"
"D=-12-12(0)=-12<0"
Then "Point(0,0)" is a saddle point.
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