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f = xy(a-x-y) = axy-yx^2-xy^2
f'<x> = ay-2xy-y^2 = y(a-2x-y)
f'<y> = ax-x^2-2xy = x(a-x-2y)
å¾é©»ç¹ (0,0), (0,a), (a,0), (a/3, a/3)
Aï¼f''<xx> = -2y, Bï¼ f''<xy> = a-2x-2y, Cï¼f''<yy> = -2x
对äºé©»ç¹ (0,0), (0,a), (a,0) ï¼AC-B^2<0, ä¸æ¯æå¼ç¹ã
对äºé©»ç¹ (a/3, a/3) ï¼A=-2a/3<0, AC-B^2 = 4a^2/9 - a^2/9 > 0,
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(a/3, a/3) 为æ大å¼ç¹ï¼ æå¤§å¼ f<max> = a^3/27ã
åæ°æ¹æ³ï¼
f = xy(a-x-y) ⤠{ [x+y+(a-x-y)]/3}^3 = a^3/27
æ大å¼å¨ x = y = a/3 æ¶åå¾ã
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