Question

已知函數(shù)y＝f(x)的圖象關(guān)于y軸對稱，且當x∈(－∞，0)時，f(x)＋xf′(x)＜0成立，a＝(2^0.2)·f(2^0.2)，b＝(log_π3)·f(log_π3)，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　因為函數(shù)y＝f(x)關(guān)于y軸對稱，所以函數(shù)y＝xf(x)為奇函數(shù)．因為[xf(x)]′＝f(x)＋xf′(x)，且當x∈(－∞，0)時，[xf(x)]′＝f(x)＋xf′(x)＜0，則函數(shù)y＝xf(x)在(－∞，0)上單調(diào)遞減；因為y＝xf(x)為奇函數(shù)，所以當x∈(0，＋∞)時，函數(shù)y＝xf(x)單調(diào)遞減．因為1＜2^0.2＜2,0＜log_π3＜1，log₃9＝2，所以0＜log_π3＜2^0.2＜log₃9，所以b＞a＞c，選A.