求函数f(x,y)=x³-4x²+2xy-y²+5的极值.
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求函数f(x,y)=x³-4x²+2xy-y²+5的极值.
![求函数f(x,y)=x³-4x²+2xy-y²+5的极值.](/uploads/image/z/17368357-13-7.jpg?t=%E6%B1%82%E5%87%BD%E6%95%B0f%28x%2Cy%29%3Dx%26sup3%3B-4x%26sup2%3B%2B2xy-y%26sup2%3B%2B5%E7%9A%84%E6%9E%81%E5%80%BC.)
f'x=3x^2-8x+2y=0
f'y=2x-2y=0--> x=y,代入上式得:3x^2-6x=0,
即x=0 or 2,y=0 or 2
A=f"xx=6x-8
C=f"yy=-2
B=f"xy=2
当x=0,y=0,A=-2,B=2,C=-2,AC-B^2=-8*(-2)-4=12>0,A
f'y=2x-2y=0--> x=y,代入上式得:3x^2-6x=0,
即x=0 or 2,y=0 or 2
A=f"xx=6x-8
C=f"yy=-2
B=f"xy=2
当x=0,y=0,A=-2,B=2,C=-2,AC-B^2=-8*(-2)-4=12>0,A
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