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#606dc80d-48ba-45f8-aaef-9a480833ee75中等解答题导数压轴题常见模型导数及其应用

41.已知函数f(x)=13x3+12ax2(a+1)x+1f(x)=\frac{1}{3}x^3+\frac{1}{2}ax^2-(a+1)x+1
(1)若f(x)f(x)的单调递减区间为[23,1][-\frac{2}{3},1],求实数aa的值;
(2)若函数y=f(x)y=f(x)[2[23]3]单调递减,求实数aa的取值范围.