已知可导函数f(x)(x∈R)满足f’(x)>f(x) ,则当a>0时,f(a)和e^af(0) 的大小关系为?A,f(a)<e^af(0) B,f(a)>e^af(0) C,f(a)=e^af(0) D,f(a)≤e^af(0)

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已知可导函数f(x)(x∈R)满足f’(x)>f(x),则当a>0时,f(a)和e^af(0)的大小关系为?A,f(a)<e^af(0)B,f(a)>e^af(0)C,f(a)=e^af(0)D,f(

已知可导函数f(x)(x∈R)满足f’(x)>f(x) ,则当a>0时,f(a)和e^af(0) 的大小关系为?A,f(a)<e^af(0) B,f(a)>e^af(0) C,f(a)=e^af(0) D,f(a)≤e^af(0)
已知可导函数f(x)(x∈R)满足f’(x)>f(x) ,则当a>0时,f(a)和e^af(0) 的大小关系为?
A,f(a)<e^af(0) B,f(a)>e^af(0) C,f(a)=e^af(0) D,f(a)≤e^af(0)

已知可导函数f(x)(x∈R)满足f’(x)>f(x) ,则当a>0时,f(a)和e^af(0) 的大小关系为?A,f(a)<e^af(0) B,f(a)>e^af(0) C,f(a)=e^af(0) D,f(a)≤e^af(0)
令 g(x) = f(x)/(e^x).
g'(x) = [f'(x) * e^x - e^x * f(x)] / (e^2x) = [f'(x) - f(x)]/(e^x) > 0
g(x) 为增函数.
因此 a>0 时,f(a)/e^a > f(0)/e^0 = f(0) => f(a) > e^af(0)
选 B.