Q. 3 N

# Verify Rolle’s theorem for each of the following functions on the indicated intervals : First, let us write the conditions for the applicability of Rolle’s theorem:

For a Real valued function ‘f’:

a) The function ‘f’ needs to be continuous in the closed interval [a,b].

b) The function ‘f’ needs differentiable on the open interval (a,b).

c) f(a) = f(b)

Then there exists at least one c in the open interval (a,b) such that f’(c) = 0.

Given function is: We know that sine function is continuous and differentiable over R.

Let’s check the values of function ‘f’ at the extremums, f(0) = 0 – 4(0)

f(0) = 0     .

We got . So, there exists a cϵ such that f’(c) = 0.

Let’s find the derivative of function ‘f.’     We have f’(c) = 0   We know     Rolle’s theorem is verified.

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