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

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

Answers (1)

Answer:

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[-2,2] 

Explanation:

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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