Sketch the graph of f(x)=1/(1+x^2)showing y-intercept, intervals where the graph increase / decrease, intervals where the graph is concave up/ down , inflexion point and stationary point

when x = 0, y = 1 that is y axis intercept

since x^2 is always + the graph slopes down from 1 to 0 at infinity and it is always in the first quadrant.

just sketch it and you will see that the rest is silly.