#### Please solve RD Sharma class 12 chapter Mean value theorem exercise 14.1 question 10 sub question (i) maths textbook solution

The Rolle’s Theorem is not applicable.

Hint:

$f:[a, b] \rightarrow R$the following three conditions of Rolle’s Theorem is satisfied.

Given:

$f(x)=[x]$ for$x \in[5,9]$

Explanation:

Rolle’s Theorem is applicable to function$f:[a, b] \rightarrow R$ the following three conditions

1. Function f is continuous in closed interval$[a, b]$
2. Function f is differentiable in open interval$(a, b)$
3. $f(a)=f(b)$

$f(x)=[x]$for$x \in[5,9]$

The greatest integer function f is neither continuous in closed interval$[5,9]$nor differentiable in open interval$(5,9)$

Also       $f(5) \neq f(9)$

Hence, the Rolle’s Theorem is not applicable to$f(x)=[x]$ for$x \in[5,9]$