f(xï¼y)=(6x-x²)(4y-y²)
令∂f/∂x=(6-2x)(4y-y²)=0ï¼å¾x₁=3ï¼y₁=0ï¼y₂=4ï¼
å令∂f/∂y=(6x-x²)(4-2y)=0ï¼å¾x₂=0, x₃=6ï¼y₃=2.
é©»ç¹ï¼M₁(3ï¼0)ï¼M₂(3ï¼4)ï¼M₃(3ï¼2)ï¼N₁(0ï¼0ï¼ï¼N₂(0ï¼2)ï¼N₃(0ï¼4)ï¼
P₁(6ï¼0)ï¼P₂(6ï¼4)ï¼P₃(6ï¼2).
A=∂²f/∂x²=-2(4y-y²)
B=∂²f/∂x∂y=(6-2x)(4-2y)
C=∂²f/∂y²=-2(6x-x²)
对ä¹ä¸ªé©»ç¹æ±åºå¯¹åºçAãBãCçå¼ï¼
å对æ¯ç»AãBãCåå«å®åºB²-ACç符å·ï¼
B²-AC<0èA>0å¾æå°å¼f(xiï¼yi);A<0å¾æ大å¼f(xiï¼yi);
B²-AC>0,æ æå¼ï¼B²-AC=0ï¼ä¸è½å³å®ã
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