# Differentiability of wave function at boundary in infinite square well

I was told in class that a wave function should have the following properties:

1. Finite and single-valued
2. Continuous
3. Differentiable
4. Square integrable

But if we consider the wave function in an infinite square well, the wave function isn't differentiable at the boundaries since $$\Psi (x)$$ is:

$$\Psi (x) =\begin{cases} \sqrt{\frac{2}{L}}\sin(\frac{n\pi x}{L}), & 0

This violates one of the properties of wave functions. So how is this an acceptable wave function?