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

##### 1 Answer

First we need to find the second derivative of $f \left(x\right)$ which is

$f ' ' \left(x\right) = 2 \cdot {x}^{-} 3$

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 $f \left(x\right) = \frac{1}{x}$

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