当a=1时,f(x)=x²-e^x
则:
f'(x)=2x-e^x
(1)当x≤0时,f'(x)0时,设:g(x)=2x-e^x,则:g'(x)=2-e^x
则:g(x)在(0,ln2)上递增,在(ln2,+∞)上递减,则g(x)的最大值是g(ln2)=2ln2-2=2(ln2-1)0,恒有g(x)0,恒有f'(x)
当a=1时,f(x)=x²-e^x
则:
f'(x)=2x-e^x
(1)当x≤0时,f'(x)0时,设:g(x)=2x-e^x,则:g'(x)=2-e^x
则:g(x)在(0,ln2)上递增,在(ln2,+∞)上递减,则g(x)的最大值是g(ln2)=2ln2-2=2(ln2-1)0,恒有g(x)0,恒有f'(x)