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令g(x)=(x-1)f(x)=(x²-1)lnx-(x-1)²
定义域x>0,且g(1)=0
g'(x)=(x²-1)/x+2xlnx-2(x-1)
g'(1)=0,x=1为g(x)的唯一极值点
g'(e)=e-1/e+2e-2(e-1)=e-1/e+2>0
g'(1/e)=1/e-e-2/e+2(1/e-1)=1/e-e-2=0
定义域x>0,且g(1)=0
g'(x)=(x²-1)/x+2xlnx-2(x-1)
g'(1)=0,x=1为g(x)的唯一极值点
g'(e)=e-1/e+2e-2(e-1)=e-1/e+2>0
g'(1/e)=1/e-e-2/e+2(1/e-1)=1/e-e-2=0
1年前
10
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