①f(x)=e^(-x)•(x²+ax+1)
f'(x)=-e^(-x)•(x²+ax+1)+e^(-x)•(2x+a)
=-e^(-x)•[x²+(a-2)x+1-a]
=-e^(-x)•(x-1)(x-1+a)
(ⅰ)当a=0时,f'(x)=-e^(-x)•(x-1)²≤0,f(x)为R上的减函数;
(ⅱ)当a>0时,令f'(x)>0,即 (x-1)(x-1+a)
①f(x)=e^(-x)•(x²+ax+1)
f'(x)=-e^(-x)•(x²+ax+1)+e^(-x)•(2x+a)
=-e^(-x)•[x²+(a-2)x+1-a]
=-e^(-x)•(x-1)(x-1+a)
(ⅰ)当a=0时,f'(x)=-e^(-x)•(x-1)²≤0,f(x)为R上的减函数;
(ⅱ)当a>0时,令f'(x)>0,即 (x-1)(x-1+a)