Q. 16
Verify Rolle’s theorem for each of the following functions:
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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