设f(x,y)=x3-3x+y2+4y+1,则f(x,y)的极值点为______,极值为_________.

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问题 设f(x,y)=x3-3x+y2+4y+1,则f(x,y)的极值点为______,极值为_________.

选项

答案(1,-2);-5

解析

f’’xx(x,y)=6sc,f’’xy(x,y)=0,f’’yy(x,y)=2,
当(x,y)=(-1,-2)时,A=-6,B=0,C=2,
因为AC-B2<0,所以(-1,-2)不是f(x,y)的极值点;
当(x,y)=(1,-2)时,A=6,B=0,C=2,
因为AC-B2>0且A>0,所以(1,-2)为f(x,y)的极小值点,
极小值为f(1,-2)=-5.
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