Answer :

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.


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