Question

已知偶函數(shù)f(x)滿足條件：當(dāng)x∈R時，恒有f(x+2)=f(x),且0≤x≤1時，有f′(x)＞0，則f(),f(),f()的大小關(guān)系是

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

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

Answer 1

B  ∵x∈R時恒有f(x+2)=f(x),∴f(x)周期為T=2.又0≤x≤1時,f′(x)＞0,

∴偶函數(shù)f(x)在［0,1］上單調(diào)遞增,在［-1,0］上單調(diào)遞減.

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

又0＜＜＜＜1,∴f()＞f()＞f(),即f()＞f()＞f().