Question

The function f, defined by f(x)= |x-2| is differentiable in [0,1].

True or false with full explanation

Answer 1

Let us show that the function $f$, defined by $f(x)= |x-2|$ is differentiable in $[0,1]$. If $x-2<0$, that is $x<2$, then $f(x)=-(x-2)=-x+2.$ In particular, for $x\in[0,1]$ we have that $f(x)=-x+2.$ Since the elementary linear function is differentiable in each point, we conclude that the function $f$ is differentiable in $[0,1]$.