Examine if Rolle's theorem is applicable to any of the following functions. Can you say something about the converse of Rolle's theorem from these example?
(i) `f(x)=[x]` for `x in [5,9]`
(ii) `f(x) = [x]` for `x in [-2,2]`
(iii) `f(x)=x^2-1` for `x in [1,2]`

Explanation

(i)
Given f(x)=[x] for x∈ [5, 9]
Since, the greatest integer function is not continuous at integral values.

So, f(x) is not continuous at x=5,6,7,8,9

So, f(x) is not continuous in [5,9].


Since, f is not continuous on [5,9].

Hence, Rolle's theorem is not applicable on given function

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