\(\displaystyle f(x)=\left\{\begin{array}{cc}x^2,&\mbox{ if }

x\leq 1\\\frac{x+1}{2}, & \mbox{ if } x>1\end{array}\right\)

Is f(x) differentiable at x=1?

I know that we have to prove

\(\displaystyle \boxed{ \lim_{\Delta x \to 0}\frac{f(1+\Delta x)-f(1)}{\Delta x}}\)

exist/does not exist at x=1. But how do I begin? It's a piece-wise function.

Thanks for your help.