#### explain solution rd sharma class 12 chapter 14 Mean Value Theoram exercise multiple choice question 4 maths

Option (c)

Hint:

Prove mean value theorem

Given: $f^{'}(x_{1})=\frac{f(b)-f(a)}{b-a}$

Solution:

Mean value theorem,

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

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

$f^{'}(x_{1})=\frac{f(b)-f(a)}{b-a}$

$a< x_{1}< b$

$\therefore f^{'}(x_{1})=\frac{f(b)-f(a)}{b-a}$

$\Rightarrow a< x_{1}< b$

Hence, option (c) is correct.