Question

Assertion :If Rolle's theorem be applied in $f\left(x\right)$, then L.M.V. theorem is also applicable for $f\left(x\right)$. Reason: Both Rolle's theorem & L.M.V. theorem can not be applied in $f\left(x\right)=\left|\sin \left|x\right|\right|$ in $[-\frac{\pi }{3},\frac{\pi }{3}]$

• 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 B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

Assertion: If Rolle's theorem be applied in $f\left(x\right)$, then L.M.V theorem is also applicable for $f\left(x\right)$

It is true because two conditions of Rolle's theorem namely

i) $f\left(x\right)$ continuous in [a,b]$

ii) $f\left(x\right)$differentiable in (a,b)$

is also true for L.M.V theorem

Reason: $f\left(x\right)=\left|\sin x\right|$ in $[-\frac{\pi }{3},\frac{\pi }{3}]$ is not continuous differentiable therefore does not follow Rolle's and L.M.V theorem

Thus, both assertion and Reason are correct but reason is not correct explanation for Assertion.