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:


on [ – 1,0]


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


Let’s check the values of ‘f’ at an extremum





f( – 1) = 0




f(0) = 0 – 0


f(0) = 0


We have got f( – 1) = f(0). So, there exists a cϵ( – 1,0) such that f’(c) = 0.


Let’s find the derivative of the function ‘f’





We have f’(c) = 0








Cosine is positive between , for our convenience we take the interval to be , since the values of the cosine repeats.


We know that value is nearly equal to 1. So, the value of the c nearly equal to 0.


So, we can clearly say that cϵ( – 1,0).


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
caricature
view all courses
RELATED QUESTIONS :

Verify the Rolle’Mathematics - Exemplar

The value of c inMathematics - Exemplar

For the function Mathematics - Exemplar

Verify the Rolle’Mathematics - Exemplar

Verify the Rolle’Mathematics - Exemplar

Discuss theRD Sharma - Volume 1

Using Rolle’s theMathematics - Exemplar

Verify the Rolle’Mathematics - Exemplar

State True Mathematics - Exemplar

Discuss the appliMathematics - Exemplar