Therefore, Rolle’s Theorem is notapplicable to those functions that do not satisfy any of the three conditionsof the hypothesis.
(i) 
It is evident that the givenfunction f (x) is not continuous at every integralpoint.
In particular, f(x)is not continuous at x = 5 and x = 9
⇒ f (x)is not continuous in [5, 9].
The differentiability of f in(5, 9) is checked as follows.
Let n be aninteger such that n ∈ (5, 9).
Since the left and right handlimits of f at x = n are notequal, f is not differentiable at x = n
∴f is not differentiable in (5, 9).
It is observed that f doesnot satisfy all the conditions of the hypothesis of Rolle’s Theorem.
Hence,Rolle’s Theorem is not applicable for
(ii) 
It is evident that the givenfunction f (x) is not continuous at every integral point.
In particular, f(x)is not continuous at x = −2 and x = 2
⇒ f (x) is not continuous in [−2, 2].
The differentiability of f in(−2, 2) is checked as follows.
Let n be aninteger such that n ∈ (−2, 2).
Since the left and right handlimits of f at x = n are notequal, f is not differentiable at x = n
∴f is not differentiable in (−2, 2).
It is observed that f doesnot satisfy all the conditions of the hypothesis of Rolle’s Theorem.
Hence,Rolle’s Theorem is not applicable for
(iii) 
It is evident that f,being a polynomial function, is continuous in [1, 2] and is differentiable in(1, 2).
∴f (1) ≠ f (2)
It is observed that f doesnot satisfy a condition of the hypothesis of Rolle’s Theorem.
Hence,Rolle’s Theorem is not applicable for