已知函数f(x)=xlnx+(a-1)x (a属于R) (1)当a=1时,求曲线y=f(x)在x=1上的切线方程(2)求函数f(x)在区间[1/e,e]上的最小值(3)若关于x的方程f(x)=2x^3-3x^2在区间[1/2,2]内有两个不相等的实数根,求实数a的取值范围
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![已知函数f(x)=xlnx+(a-1)x (a属于R) (1)当a=1时,求曲线y=f(x)在x=1上的切线方程(2)求函数f(x)在区间[1/e,e]上的最小值(3)若关于x的方程f(x)=2x^3-3x^2在区间[1/2,2]内有两个不相等的实数根,求实数a的取值范围](/uploads/image/z/2491761-57-1.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dxlnx%2B%28a-1%29x+%28a%E5%B1%9E%E4%BA%8ER%29+%281%29%E5%BD%93a%3D1%E6%97%B6%2C%E6%B1%82%E6%9B%B2%E7%BA%BFy%3Df%28x%29%E5%9C%A8x%3D1%E4%B8%8A%E7%9A%84%E5%88%87%E7%BA%BF%E6%96%B9%E7%A8%8B%282%29%E6%B1%82%E5%87%BD%E6%95%B0f%28x%29%E5%9C%A8%E5%8C%BA%E9%97%B4%5B1%2Fe%2Ce%5D%E4%B8%8A%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC%283%29%E8%8B%A5%E5%85%B3%E4%BA%8Ex%E7%9A%84%E6%96%B9%E7%A8%8Bf%28x%29%3D2x%5E3-3x%5E2%E5%9C%A8%E5%8C%BA%E9%97%B4%5B1%2F2%2C2%5D%E5%86%85%E6%9C%89%E4%B8%A4%E4%B8%AA%E4%B8%8D%E7%9B%B8%E7%AD%89%E7%9A%84%E5%AE%9E%E6%95%B0%E6%A0%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)
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