Discuss the applicability for Rolle’s theorem, when:f(x) = [x] on [-

1.	Discuss the applicability for Rolle’s theorem, when:f(x) = [x] on [-1, 1], where [x] denotes the greatest integer not exceeding x
Answer» Condition (1): Since, f(x) = [x] which is discontinuous at x = 0 ⇒ f(x) = [x] is not continuous on [-1,1]. Condition (1) of Rolle’s theorem is not satisfied. So, Rolle’s theorem is not applicable.

Discuss the applicability for Rolle’s theorem, when:f(x) = [x] on [-1, 1], where [x] denotes the greatest integer not exceeding x

Answer»

Condition (1):

Since, f(x) = [x] which is discontinuous at x = 0

⇒ f(x) = [x] is not continuous on [-1,1].

Condition (1) of Rolle’s theorem is not satisfied.

So, Rolle’s theorem is not applicable.