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Math Help - Differentiability of the function

  1. #1
    mx-
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    Differentiability of the function

    Could someone please confirm if the following functions is differentiable for all x?

    f(x)=\left\{\begin{array}{cc}1-x,&\mbox{ if }<br />
x<0\\1-x^2, & \mbox{ if } x\geq 0\end{array}\right.

    g(x)=\left\{\begin{array}{cc}x+1,&\mbox{ if }<br />
x<1\\3-x, & \mbox{ if } x\geq 1\end{array}\right.

    I think f(x) is differentiable for all x but not for g(x).

    Could someone please confirm ASAP.
    Thanks
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  2. #2
    Moo
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    Hello,

    I would have answered the same thing...

    The functions are both continuous. But if we study the derivatives, we have the same limit for f at x~0, not the same (-1 and 1) for g at x~1
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