Q. 3 B5.0( 2 Votes )

# Verify Rolle’s theorem for each of the following functions on the indicated intervals :f(x) = sin 2x on [0, π/2]

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 fuction is:

f(x) = sin2x on We know that sine function is continuous and differentiable on R.

Let’s find the values of function at extremum,

f(0) = sin2(0)

f(0) = sin0

f(0) = 0   We got , so there exist a such that f’(c) = 0.

Let’s find the derivative of f(x)  f’(x) = 2cos2x

We have f’(c) = 0,

2cos2c = 0  Rolle’s theorem is verified.

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