Q. 3 D5.0( 1 Vote )

# Verify Roll

Answer :

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:

f(x) = exsinx on [0, ]

We know that exponential and sine functions are continuous and differentiable on R.

Let’s find the values of the function at an extremum,

f(0) = e0sin(0)

f(0) = 1×0

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

Let’s find the derivative of f(x)  f’(x) = ex(sinx + cosx)

We have f’(c) = 0,

ec(sinc + cosc) = 0

sinc + cosc = 0     Rolle’s theorem is verified.

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