Question

若對任意實(shí)數(shù)x，有¦(―x)=―¦(x)，g(―x)=g(x)，且x>0時(shí)¦′ (x)>0，g′ (x)>0，則x<0時(shí)

A．¦′(x)>0，g′ (x)>0	B．¦′(x)>0，g′ (x)<0
C．¦′(x)<0，g′ (x)>0	D．¦′(x)<0，g′ (x)<0

Answer 1

B

由題意函數(shù)f(x)為奇函數(shù)，g(x)為偶函數(shù)，∵x>0時(shí)¦′ (x)>0，g′ (x)>0，∴函數(shù)f(x)在（0,+∞)上單調(diào)遞增，函數(shù)g(x)在（0,+∞)上單調(diào)遞增，根據(jù)奇偶函數(shù)單調(diào)性結(jié)論可知，當(dāng)x<0時(shí)，函數(shù)f(x)單調(diào)遞增，g(x)單調(diào)遞減，即¦′ (x)>0，g′ (x)<0，故選B