已知定义在R上的可导函数f(x)的导函数为f'(x),满足f'(x)>f(x),则当a》0时f(a)和e^af(0)的大小

令g(x) = e^{-x)*f(x),对g(x)求导
g'(x) = e^{-x}*[f(x) - f'(x)] < 0,所以g(x)是减函数,于是
a >= 0时,
g(a) <= g(0),即
e^{-a}*f(a) <= f(0)
即
f(a) <= f(0)*e^{-a}
等号成立当且仅当a = 0