Question

What are the points of inflection, if any, of `f(x)=1/x`?

Answer 1

First we need to find the second derivative of `f(x)` which is

`f''(x)=2*x^-3`

The second derivative is never zero.
The second derivative is undefined when `x=0`

The point `x=0` does not belong to the domain of `f(x)=1/x`

Therefore, there are No inflection points due to the fact that the original function, f, is not defined at `0`.