Question

Show that f(x) = |x-1| is not differentiable at x=1

Answer 1

if x-1>0 => x>1, then f(x)=x-1 => f'(x)=1
if x-1<0 => x<1, then f(x)=-(x-1) => f'(x)=-1
therefore f is not differentiable at x=1

Answer 2

limit from the right doesnt match the limit from the left; so limit does not exist; no limit, no derivative

Answer 3

right

Answer 4

thanks guys.