When y'=0 and x=0,
When x
So the function monotonically decreases at (negative infinity, 0) and monotonically increases at (0, positive infinity). The vertex is x=0.
y"=[2( 1+x？ )? -8x？ ( 1+x？ )]/( 1+x？ )^4=2( 1+x？ )( 1-3x？ )/( 1+x？ )^4
1-3x? & gt0, that is, the interval on [-(root number 3)/3, (root number 3)/3] is concave, and other intervals are convex.
The inflection point is x=- (root number 3)/3, and x= (root number 3)/3.