设f(x)=x^3-3/2(a+1)X^2+3ax+1,(2)若函数f(x)在区间(1,4)内单调递减,求a的取值范

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设f(x)=x^3-3/2(a+1)X^2+3ax+1,(2)若函数f(x)在区间(1,4)内单调递减,求a的取值范
设f(x)=x^3-3/2(a+1)X^2+3ax+1,(2)若函数f(x)在区间(1,4)内单调递减,求a的取值范

设f(x)=x^3-3/2(a+1)X^2+3ax+1,(2)若函数f(x)在区间(1,4)内单调递减,求a的取值范
由f'(x)=3x^2-3(a+1)x+3a=3(x-a)(x-1)=0, 得极值点x=1, a
若a>1, 则f(x)只在(1,a)单调减
若a