The Rolle's theorem is not applicable to f x = x , 0 ≤ x ≤ 1 2 - x , 1 ≤ x ≤ 2 on [ 0 ,   2 ] because

Step-by-step solution

Rolle's Theorem is applicable for a function y = f x , x ∈ a , b , if i )   f x is continuous for all x ∈ a , b i i ) f x is differentiable for all x ∈ a , b i i i ) f a = f b Here,   f 0 = f 2 Now, f x is defined for all x ∈ 0 , 2 & is continuous in 0 , 2 Also, f x has a sharp corner at x = 1 , so it is not differentiable at x = 1 , so f x is not differentiable in 0 , 2 .