Would I be right in saying that the function

$\displaystyle f(x)=\left\{\begin{array}{ccc}1,&\mbox{ if }

{x}=0\\x+1, & \mbox{ if } -2<x<0\\x^{-1}(1+\frac{1}{x})^{-1}, & \mbox{ otherwise }\end{array}\right.$

Is continuous everywhere but not differentiable at x=-2?

Thanks for any help