Q. 155.0( 2 Votes )

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

Answer :

Condition (1):

Since, f(x)=sin3x is a trigonometric function and we know every trigonometric function is continuous.

⇒ f(x)= sin3x is continuous on [0,π].

Condition (2):

Here, f’(x)= 3cos3x which exist in [0,π].

So, f(x)= sin3x is differentiable on (0,π).

Condition (3):

Here, f(0)=sin0=0

And f(π)=sin3π=0

i.e. f(0)=f(π)

Conditions of Rolle’s theorem are satisfied.

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

i.e. 3cos3c =0

i.e.

i.e.

Value of

Thus, Rolle’s theorem is satisfied.

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