Answer :

Condition (1):


Since, f(x)=sinx+cosx is a trigonometric function and we know every trigonometric function is continuous.


f(x)= sinx+cosx is continuous on .


Condition (2):


Here, f’(x)= cosx-sinx which exist in .


So, f(x)= sinx+cosx is differentiable on


Condition (3):


Here, f(0)=sin0+cos0=1


And


i.e.


Conditions of Rolle’s theorem are satisfied.


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


i.e. cosc-sinc =0


i.e.


Value of


Thus, Rolle’s theorem is satisfied.


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