已知函数f(x)=(x²-2ax+a²)lnx a∈R,1)当a=0时,求f(x)单调区间2)当a=-1时,令F(x)=[f(x)/x+1]+x-lnx证明F(x)大于等于e^-2.3)若函数f(x)不存在极值点,求实数a的取值范围
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![已知函数f(x)=(x²-2ax+a²)lnx a∈R,1)当a=0时,求f(x)单调区间2)当a=-1时,令F(x)=[f(x)/x+1]+x-lnx证明F(x)大于等于e^-2.3)若函数f(x)不存在极值点,求实数a的取值范围](/uploads/image/z/5220297-9-7.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3D%28x%26%23178%3B-2ax%2Ba%26%23178%3B%29lnx+a%E2%88%88R%2C1%29%E5%BD%93a%3D0%E6%97%B6%2C%E6%B1%82f%28x%29%E5%8D%95%E8%B0%83%E5%8C%BA%E9%97%B42%29%E5%BD%93a%3D-1%E6%97%B6%2C%E4%BB%A4F%28x%29%3D%5Bf%28x%29%2Fx%2B1%5D%2Bx-lnx%E8%AF%81%E6%98%8EF%28x%29%E5%A4%A7%E4%BA%8E%E7%AD%89%E4%BA%8Ee%5E-2.3%29%E8%8B%A5%E5%87%BD%E6%95%B0f%28x%29%E4%B8%8D%E5%AD%98%E5%9C%A8%E6%9E%81%E5%80%BC%E7%82%B9%2C%E6%B1%82%E5%AE%9E%E6%95%B0a%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4)
已知函数f(x)=(x²-2ax+a²)lnx a∈R,1)当a=0时,求f(x)单调区间2)当a=-1时,令F(x)=[f(x)/x+1]+x-lnx证明F(x)大于等于e^-2.3)若函数f(x)不存在极值点,求实数a的取值范围
已知函数f(x)=(x²-2ax+a²)lnx a∈R,1)当a=0时,求f(x)单调区间
2)当a=-1时,令F(x)=[f(x)/x+1]+x-lnx证明F(x)大于等于e^-2.
3)若函数f(x)不存在极值点,求实数a的取值范围
已知函数f(x)=(x²-2ax+a²)lnx a∈R,1)当a=0时,求f(x)单调区间2)当a=-1时,令F(x)=[f(x)/x+1]+x-lnx证明F(x)大于等于e^-2.3)若函数f(x)不存在极值点,求实数a的取值范围
解 当a=0时 f(x)=x²lnx f¹(x)=2x²lnx+x=x(2xlnx+1)求出0点,然后求出单调区间
(2) 当a=-1时 f(x)=(x²+2 x+1)lnx F(x)=[f(x)/x+1]+x-lnx
=[(x²+2 x+1)lnx/x+1]+x-lnx≥e^-2.=1/e²
化简后得(x+1)(lnx +1)+lnx/x≥1/e²