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·æäºé¶è¿ç»çå导æ°çæ¡ä»¶ä¸ï¼è®¾f''xx=Aï¼f''xy=Bãf''yy=C;
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f'x=2xy(4-x-y)-x^2y=0, 令x,yâ 0å³8-3x-2y=0.....(1)
f'y=x^2(4-x-y)-x^2y=0, å³ï¼4-x-2y=0....(2)
(1)-(2),å¾ï¼4-2x=0; 解å¾ï¼x=2ï¼ ä»£å
¥(2),å¾ï¼y=1ï¼
f''xx=2y(4-x-y)-2xy-2xy=2y(4-x-y)-4xy=2*1*(4-2-1)-4*2*1=-6<0ï¼
f''xy=2x(4-x-y)-2xy-x^2=2*2(4-2-1)-2*2-4=-6;
f''yy=-x^2-x^2=-2x^2=-8;
(-6)*(-8)-(-6)^2=12>0ï¼ ä¸ºæå¼ç¹ï¼å 为f''xx<0, 为æ大å¼ã
f(2,1)=2^2*1(4-2-1)=4, 为å½æ°çæ大å¼ã
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