Discuss the applicability for Rolle’s theorem, when:
Condition (1):
Since, f(x)=x1/2 is a polynomial and we know every polynomial function is continuous for all xϵR.
⇒ f(x)= x1/2 is continuous on [-1,1].
Condition (2):
Here, which does not exist at x=0 in [-1,1].
f(x)=x1/2 is not differentiable on (-1,1).
Condition (2) of Rolle’s theorem is not satisfied.
So,Rolle’s theorem is not applicable.