Do points of inflection have to be differentiable?

$f \left(x\right) = \left\{\begin{matrix}{x}^{2} & \mathmr{if} x < 0 \\ \sqrt{x} & \mathmr{if} x \ge 0\end{matrix}\right.$
is concave upward on $\left(- \infty , 0\right)$ and concave downward on $\left(0 , \infty\right)$ and is continuous at $x = 0$, so $\left(0 , 0\right)$ is an inflection point but not differentiable there.