Question

What are the points of inflection of `f(x)=1/(1+x^2)`?

Answer 1

The inflection points could be found by calculating the roots of the second derivative (if there are any).

Hence we have that

`d^2f(x)/dx^2=0=>(6x^2-2)/(x^2+1)^3=0=>x=1/sqrt3 or x=-1/sqrt3`

So the inflection points are

`(1/sqrt3,f(1/sqrt3))` and `(-1/sqrt3,f(-1/sqrt3))`