Answer
At an inflection point we have $f{\rm{''}}\left( x \right) = 0$. Hence, the curvature is zero at an inflection point.
Work Step by Step
We have $y = f\left( x \right)$.
By Eq. (5) of Theorem 2, the curvature is given by
$\kappa \left( x \right) = \frac{{|f{\rm{''}}(x|}}{{{{\left( {1 + f'{{\left( x \right)}^2}} \right)}^{3/2}}}}$
By Theorem 2 of Section 4.4, at an inflection point we have $f{\rm{''}}\left( x \right) = 0$. Hence, the curvature is zero at an inflection point.
