Question

Question 2: Examine if Rolle’s theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle’s theorem from these example? (i) f (x) = [x] for x ∈ [5, 9] (ii) f (x) = [x] for x ∈ [– 2, 2] (iii) f (x) = x2 – 1 for x ∈ [1, 2]

Class 12 - Math - Continuity and Differentiability

Answer 1

1) The given function is greatest integer function thus the given function is not differentiable and continuous.

hence Rolle’s theorem is not applicable.

2) the given function is greatest integer function the given function is not differentiable and continuous hence Rolle’s theorem is not applicable.

3) f(x) = x²-1
=> f(1) = 1²-1 => 0
f(2) = 2²-1 => 3
hence f(1)≠f(2)


Hence, Rolle’s theorem is not applicable.