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Math Help - continuous/differentiable

  1. #1
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    continuous/differentiable

    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
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by hmmmm View Post
    Is continuous everywhere but not differentiable at x=-2?
    Right. Besides:

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

    Regards.

    Fernando Revilla
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  3. #3
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    yeah that is what I looked at, thanks
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