Q. 16

# Verify Rolle’s theorem for each of the following functions: 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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