Mathematics - Continuity - Differentiability Question with Solution | TestHub

The given function is

$f\left(x\right)=\left\{\begin{array}{ll}0,& 0\le x<1\\ 1,& 1\le x<2\end{array}\right.$

Now, $\mathrm{LHD}=\underset{x\to 1^{-}}{\lim }\frac{f\left(x\right)-f\left(1\right)}{x-1}=\underset{x\to 1^{-}}{\lim }\frac{0-1}{x-1}$

Which does not exist 

$\therefore f$ is not derivable at $x=1$.