已知a>=0,函数f(x)=(x^2-2ax)e^x,设在f(x)在区间[-1,1]上是单调函数,求a的取值范围.

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f(x)=(x²-2ax)e^x
f'(x)=(x²-2ax+2x-2a)e^x
令g(x)=x²+(2-2a)x-2a
g(0)=-2a<0
则丛亏笑g(x)≤0恒空差成立
所以渗含g(-1)≤0,g(1)≤0
所以a≥3/4

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对f(x)求导得f'(x)=(x^2-2ax+2x-2a)e^x 因为f(x)在[-1,1]单调，则f'(x)>=0或者f(x)<=0　用分离变量的尘早方派兄雀法分别解得尘芦为无解和a>=3/2…故a>=3/2

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a≥1或a ≤－1

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