Question

已知偶函数f(x)满足条件：当x∈R时，恒有f(x+2)=f(x),且0≤x≤1时，有f′(x)＞0，则f(),f(),f()的大小关系是

A.f()＞f()＞f()                      B.f()＞f()＞f()

C.f()＞f()＞f()                      D.f()＞f()＞f()

Answer 1

B  ∵x∈R时恒有f(x+2)=f(x),∴f(x)周期为T=2.又0≤x≤1时,f′(x)＞0,

∴偶函数f(x)在［0,1］上单调递增,在［-1,0］上单调递减.

f()=f(6)=f(),f()=f(6)=f(),f()=f(6+)=f(),

又0＜＜＜＜1,∴f()＞f()＞f(),即f()＞f()＞f().