I am stuck with the following problem:

If $u(x,t)$ satisfies the wave equation:  

$u\_{tt}=c^2u\_{xx}, x \in \Bbb R,t>0$ ,with initial conditions 

$u(x,0)=\begin{cases}\sin\dfrac{\pi x}{c}&0\leq x\leq c\\0&\text{elsewhere}\end{cases}$

and $u\_t(x,0)=0$ $\forall x$ , then for a given $t>0$ , 

> 
> 1. there are values of $x$ at which $u(x,t)$ is discontinuous
> 2. $u(x,t)$ is continuous,but $u\_x(x,t)$ is not continuous
> 3. $u(x,t)$ and $u\_x(x,t)$ are continuous,but $u\_{xx}(x,t)$ is not continuous
> 4. $u(x,t)$ is smooth for all $x$ .
> 
> 
> 

I am studying the Cauchy problem for the wave equation $n=2$ ;
$$\begin{cases}u\_{tt}=\alpha^{2} u\_{xx}, x \in\mathbb{R}, t>0\\[8pt]
u(x,0)=f(x), x\in\mathbb{R}\\[8pt]
u\_{t}(x,0)=g(x), x\in\mathbb{R}
\end{cases}$$ 

By d´Alembert's formula we know that 

$u(x,t)=\dfrac{f(x+\alpha t)+f(x-\alpha t)}{2} +\dfrac{1}{2\alpha} \displaystyle\int^{x+\alpha t}\_{x-\alpha t}g(s)ds=\dfrac{1}{2}[f(x+ct)+f(x-ct)]$ , since here $\alpha=c$ , $g(s)=0$ . 

Now I am not sure how to progress hereon. Can someone point me in the right direction? Thanks in advance for your time.