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【简答题】
定义在D上的函数f(x),如果满足:对任意x∈D,存在常数M,f(x)≥M成立,则称f(x)是D上的有界函数,其中M称为函数f(x)的下界.已知函数f(x)=(x 2 -3x+3)?e x ,其定义域为[-2,t](t>-2),设f(-2)=m,f(t)=n. (1)试确定t的取值范围,使得函数f(x)在[-2,t]上为单调递增函数; (2)试判断m,n的大小,并说明理由;并判断函数f(x)在定义域上是否为有界函数,请说明理由; (3)求证:对于任意的t>-2,总存在x 0 ∈(-2,t)满足 f′( x 0 ) e x 0 = 2 3 (t-1) 2 ,并确定这样的x 0 的个数.
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