已知可导函数f(x)(x∈R)满足f′(x)>f(x),则当a>0时,f(a)和eaf(0)大小关系为( ) A.f(a)<eaf(0) B.f(a)>eaf(0) C.f(a)=eaf(0) D.f(a)≤eaf(0)
问题描述:
已知可导函数f(x)(x∈R)满足f′(x)>f(x),则当a>0时,f(a)和eaf(0)大小关系为( )
A. f(a)<eaf(0)
B. f(a)>eaf(0)
C. f(a)=eaf(0)
D. f(a)≤eaf(0)
答
由题意知,可设函数f(x)=e2x,
则导函数f′(x)=2•e2x,显然满足f'(x)>f(x),
f(a)=e2a,eaf(0)=ea,当a>0时,显然 e2a>ea ,即f(a)>eaf(0),
故选 B.