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

Answers (1)

Answer:

The Rolle’s Theorem is not applicable.

Hint:

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

Given:

               f(x)=[x] forx \in[5,9]

Explanation:

Rolle’s Theorem is applicable to functionf:[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]forx \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 tof(x)=[x] forx \in[5,9]

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