对y=x/(x^2 +1)求导,y ' =1/(x^2+1)- 2x^2 / (x^2 +1)^2=(1-x^2) / (x^2 +1)^2,令y'>=0,解得单调增区间[-1,1],递减区间是（负无穷,-1）U（1,正无穷）,当x=1时,取最大值1/2；当x=-1时,取最小值-1/2.