Question

Assertion :$\left|x^3\right|$ is differentiable at $x=0$ Reason: If f(x) is differentiable at $x=a$ then $\left|f\left(x\right)\right|$ is also differentiable at $x=a$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is C Assertion is correct but Reason is incorrect

Clearly $|x^3|$ is differentiable at $x=0\Rightarrow$ Assertion is correct.
And Reason is incorrect. Example $f\left(x\right)=x$ is differentiable at $x=0$ but $|x|$ is not differentiable at $x=0$