Discuss the applicability for Rolle’s theorem, when: , where [x] denotes the greatest integer not exceeding x

Question

Philoid · Accepted 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.