# Differentiability of the function

• Apr 6th 2008, 04:03 AM
mx-
Differentiability of the function
Could someone please confirm if the following functions is differentiable for all x?

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

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

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

Thanks
• Apr 6th 2008, 04:25 AM
Moo
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