f(x)=e^x-x²+2axf'(x)=e^x-2x+2a.f''(x)=e^x-2.x∈(-∞,ln2)时,f''(x)＜0,x∈(ln2,+∞)时,f''(x)＞0.故f'(x)在(-∞,ln2)递减,(ln2,+∞)递增.因此,f'(x)min=f'(ln2)=2-2ln2+2a=2(a+1-ln2).∵a＞ln2-1∴a+1-ln2＞...