Assertion (A) $f(x)=|x|$ is differentiable at $x=a \neq 0$ and continuous but not differentiable at $x=0$ Reason (R) If a function is differentiable at a point, then it is continuous at the point. But converse is not true.

• Correct answer
  A

  $\mathrm{A}$ is correct, $\mathrm{R}$ is correct, $\mathrm{R}$ is correct explanation of $\mathrm{A}$
• B

  A is correct, $\mathrm{R}$ is correct, but $\mathrm{R}$ is not correct explanation of $\mathrm{A}$.
• C

  $\mathrm{A}$ is correct, $\mathrm{R}$ is false
• D

  A is false, $R$ is correct.

Solution

From the graph of $f(x)=|x|$, it is clear that $f(x)$ is everywhere continuous but not differentiable at $x=0$, due to sharp edge. $\therefore f(x)=|x|$ is differentiable if $x \in R-\{0\}$.

Hence, the correct answer is option: 'A'.