已知函数f(x)=(2-a)lnx+1/x+2ax,问当a

问题描述:

已知函数f(x)=(2-a)lnx+1/x+2ax,问当a

f'﹙x﹚=﹙2-a﹚/x-1/x²+2a
=﹙2x-1﹚﹙ax+1﹚/x²
=2a﹙x-1/2﹚﹙x+1/a﹚/x²
①当-2<a<0时,-1/a>1/2
函数在﹙0,1/2﹚上递减,在﹙1/2,-1/a﹚上递增,在﹙-1/a,+∞﹚上递减
②当a=-2时,导函数≤0
函数在﹙0,+∞﹚上递减
③当a<-2时,0<-1/a<1/2
函数在﹙0,-1/a﹚上递减,在﹙-1/a,1/2﹚ 上递增,在﹙1/2,+∞﹚上递减