continuous/differentiable

**hmmmm** · December 8th 2010, 07:37 AM

Would I be right in saying that the function

$f(x)=\left\{\begin{array}{ccc}1,&\mbox{ if }<br /> {x}=0\\x+1, & \mbox{ if } -2<x<0\\x^{-1}(1+\frac{1}{x})^{-1}, & \mbox{ otherwise }\end{array}\right.$

Is continuous everywhere but not differentiable at x=-2?
Thanks for any help

**FernandoRevilla** · December 8th 2010, 08:03 AM

Originally Posted by hmmmm

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

Right. Besides:

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

Regards.

Fernando Revilla

**hmmmm** · December 8th 2010, 09:19 AM

yeah that is what I looked at, thanks

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