Question

Test the derivability at a point.
if f(x)={(2-x,for1≤x≤2)(x,for0 14 years ago

Answer 1

this is much easier than it seems. take the derivative and get two expression
\[f'(x) = \left\{\begin{array}{rcc}
1 & \text{if} & 0<x<1 \\
-1& \text{if} & 1<x<2
\end{array}
\right.
\]
and since they do not agree at 1, there the derivative does not exist there

Answer 2

Also sketching a graph will help you see what's going on. Derivatives don't exist where the graph has 'corners', such as this one does.