Condition (1):

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].

Condition (2):

Here, f’(x)=2x which exist in [-1,1].

So, f(x)=x² is differentiable on (-1,1).

Condition (3):

Here, f(-1)=(-1)²=1

And f(1)=1¹=1

i.e. f(-1)=f(1)

Conditions of Rolle’s theorem are satisfied.

Hence, there exist at least one cϵ(-1,1) such that f’(c)=0

i.e. 2c=0

i.e. c=0

Value of c=0ϵ(-1,1)

Thus, Rolle’s theorem is satisfied.