Question

已知a=2^0.2，b=0.4^0.2，c=0.4^0.6，則（　�。�

A．a(chǎn)＞b＞c

B．a(chǎn)＞c＞b

C．c＞a＞b

D．b＞c＞a

Answer 1

分析：分別考查指數(shù)函數(shù)y=0.4^x，函數(shù)為減函數(shù)；冪函數(shù)y=x^0.2，函數(shù)為增函數(shù)，從而可得結(jié)論．

解答：解：考查指數(shù)函數(shù)y=0.4^x，函數(shù)為減函數(shù)，∵0.2＜0.6，∴0.4^0.2＞0.4^0.6，∴b＞c
考查冪函數(shù)y=x^0.2，函數(shù)為增函數(shù)，∵2＞0.4，∴2^0.2＞0.4^0.2，∴a＞b
∴a＞b＞c
故選A．

點(diǎn)評(píng)：本題考查大小比較，考查函數(shù)模型的選擇，解題的關(guān)鍵在于選擇恰當(dāng)?shù)暮瘮?shù)模型，明確其單調(diào)性．