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Provide solution for RD Sharma math class 12 chapter Mean value theorem exercise 14.1 question 10 sub question (ii)

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The Rolle’s Theorem is not applicable.


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


               f(x)=[x] for x \in[-2,2] 


Rolle’s Theorem is applicable to functionf:[a, b] \rightarrow Rthe following three conditions

  1. Functionf 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[-2,2]

The greatest integer function f is neither continuous in closed interval[-2,2] nor differentiable in open interval(-2,2)

Also       f(-2) \neq f(2)

Hence, the Rolle’s Theorem is not applicable tof(x)=[x] forx \in[-2,2]

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