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]

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 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.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses