The function $f\left(x\right)=\left\{\begin{array}{c}{x}^2,\text{ for }x<1\\ 2-x,\text{ for }x\ge 1\end{array}\right.$is:

Given: $f\left(x\right)=\left\{\begin{array}{l}{x}^2,\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\text{ for }x<1\\ 2-x,\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\text{ for }x\ge 1\end{array}\right.$
Graph of this function is

 

From the graph, At the point A(1,1), we can't draw a tangent. 
Hence, f(x) is not differentiable at x=1.