Question

Assertion :Let $f\left(x\right)=\left|x\right|$, $x\ne 0$ then $f^{\prime }\left(x\right)=\frac{\left|x\right|}{x}$ Reason: $f\left(x\right)=x$ if $x\ge 0$, $f\left(x\right)=-x$ if $x<0$

• 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 A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

$\therefore$ $f\left(x\right)=\{\begin{array}{cc}x& \text{if}x\ge 0\\ -x& \text{if}x<0\end{array}$
$\therefore$ $f^{\prime }\left(x\right)=\{\begin{array}{cc}1,& x>0i.e.\frac{\left|x\right|}{x},x>0\\ -1& x<0i.e.\frac{\left|x\right|}{x},x<0\end{array}$
$=\frac{\left|x\right|}{x}(x\ne 0)$.