# Thread: continuous/differentiable

1. ## continuous/differentiable

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

2. Originally Posted by hmmmm
Is continuous everywhere but not differentiable at x=-2?
Right. Besides:

$\displaystyle f'_+(-2)=1,\;f'_-(-2)=-1$ .

Regards.

Fernando Revilla

3. yeah that is what I looked at, thanks