Since, f(x)=x2 is a polynomial and we know every polynomial function is continuous for all xϵR.
⇒ f(x)=x2 is continuous on [-1,1].
Here, f’(x)=2x which exist in [-1,1].
So, f(x)=x2 is differentiable on (-1,1).
Conditions of Rolle’s theorem are satisfied.
Hence, there exist at least one cϵ(-1,1) such that f’(c)=0
Value of c=0ϵ(-1,1)
Thus, Rolle’s theorem is satisfied.
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