Question

已知函數(shù)y＝f(x)的圖象關(guān)于y軸對(duì)稱，且當(dāng)x∈(－∞，0)時(shí)，f(x)＋xf′(x)＜0成立，a＝(20.2)·f(20.2)，b＝(logπ3)·f(logπ3)，c＝(log39)·f(log39)，則a，b，c的大小關(guān)系是(　　)

A．b＞a＞c B．c＞a＞b

C．c＞b＞a D．a＞c＞b

 

Answer 1

A

【解析】因?yàn)楹瘮?shù)y＝f(x)關(guān)于y軸對(duì)稱，所以函數(shù)y＝xf(x)為奇函數(shù)．因?yàn)?/span>[xf(x)]′＝f(x)＋xf′(x)，且當(dāng)x∈(－∞，0)時(shí)，[xf(x)]′＝f(x)＋xf′(x)＜0，則函數(shù)y＝xf(x)在(－∞，0)上單調(diào)遞減；因?yàn)?/span>y＝xf(x)為奇函數(shù)，所以當(dāng)x∈(0，＋∞)時(shí)，函數(shù)y＝xf(x)單調(diào)遞減．因?yàn)?/span>1＜20.2＜2,0＜logπ3＜1，log39＝2，所以0＜logπ3＜20.2＜log39，所以b＞a＞c，選A.