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

Condition (1):

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

⇒ f(x)=cosx is continuous on .

Condition (2):

Here, f’(x)=-sinx which exist in .

So, f(x)=cosx is differentiable on .

Condition (3):

Here,

And

i.e.

Conditions of Rolle’s theorem are satisfied.

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

i.e. -sinc=0

i.e. c=0

Value of

Thus, Rolle’s theorem is satisfied.