Answer :

Condition (1):


Since, f(x)=x2-x-12 is a polynomial and we know every polynomial function is continuous for all xϵR.


f(x)= x2-x-12 is continuous on [-3,4].


Condition (2):


Here, f’(x)=2x-1 which exist in [-3,4].


So, f(x)= x2-x-12 is differentiable on (-3,4).


Condition (3):


Here, f(-3)=(-3)2-3-12=0


And f(4)=42-4-12=0


i.e. f(-3)=f(4)


Conditions of Rolle’s theorem are satisfied.


Hence, there exist at least one cϵ(-3,4) such that f’(c)=0


i.e. 2c-1=0


i.e.


Value of


Thus, Rolle’s theorem is satisfied.


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