Question

Assertion :If both functions $f\left(t\right)$ and $g\left(t\right)$ are continuous on the closed interval $[a,b]$, differentiable on the open interval $(a,b)$ and $g^{\prime }\left(t\right)$ is not zero on that open interval, then there exists some $c$ in $(a,b)$ such that $\frac{f^{\prime }\left(c\right)}{g^{\prime }\left(c\right)}=\frac{f\left(b\right)-f\left(a\right)}{g\left(b\right)-g\left(a\right)}$ Reason: If $f\left(t\right)$ and $g\left(t\right)$ are continuous and differntiable in $[a,b]$, then there exists some $c$ in $(a,b)$ such that $f^{\prime }\left(c\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a}$ and $g^{\prime }\left(c\right)=\frac{g\left(b\right)-g\left(a\right)}{b-a}$ from Lagrange's mean value theorm.

• 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

from theorem
assertion is correct.
but reason is incorrect because there is given close interval for derivative and open for continous which is not lagrang's theorem.