(i) f(x) = |x] being greatest integer function it is not differentiable at integral points. 

Hence not continuous on integral points 

∴ f (x) is not continuous [5, 9] 

Rolle’s theorem is not applicable to f (x) in [5,9] 

How ever f’ (x) = 0 ∀ non integral values in [5, 9] thus converse of Rolle’s theorem is not true.

(ii) f (x) = |x] being greatest integer function it is not differentiable at integral points. 

Hence not continuous on integral points 

∴ f (x) is not continuous [-2, 2] 

Rolle’s theorem is not applicable to f (x) in [-2,2] 

How ever f’ (x) = 0 ∀ non integral values in [-2, 2] thus converse of Rolle’s theorem is not true.

(iii) f (x) = x² – 1 being polynomial function f(x) is differentiable ∀ x ∈ [1, 2] 

∴ f (x) is continuous is [1, 2] 

Also f’ (x) exist, f (x) is derivable on (1, 2) 

f(1) = (1)² – 1 = 0, f(2) = (2)² – 1 =3 

f(1) ≠ f(2) 

Since all the conditions are not satisfied, the Rolle’s theorem is not applicable in the given intervals. 

Thus the converse of Rolle’s theorem does not hold. That is if the condition of Rolle’s theorem are not satisfied by a function f (x) on some interval [a, b] then f’ (x) may or may not be zero in some point in (a, b).