Discuss the applicability for Rolle’s theorem, when:

Condition (1):

Since, f(x)=x^1/2 is a polynomial and we know every polynomial function is continuous for all xϵR.

⇒ f(x)= x^1/2 is continuous on [-1,1].

Condition (2):

Here, which does not exist at x=0 in [-1,1].

f(x)=x^1/2 is not differentiable on (-1,1).

Condition (2) of Rolle’s theorem is not satisfied.

So,Rolle’s theorem is not applicable.