Q. 14

Verify Rolle’s theorem for each of the following functions:

Answer :

Condition (1):

Since, f(x)=cos2x is a trigonometric function and we know every trigonometric function is continuous.

f(x)= cos2x is continuous on [0,π].

Condition (2):

Here, f’(x)= -2sin2x which exist in [0,π].

So, f(x)=cos2x is differentiable on (0,π).

Condition (3):

Here, f(0)=cos0=1

And f(π)=cos2π=1

i.e. f(0)=f(π)

Conditions of Rolle’s theorem are satisfied.

Hence, there exist at least one cϵ(0,π) such that f’(c)=0

i.e. -2sin2c =0

i.e. 2c=π


Value of

Thus, Rolle’s theorem is satisfied.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
How to find Maxima & Minima?43 mins
Interactive quizz on tangent and normal, maxima and minima43 mins
Interactive quiz on maxima and minima48 mins
Tangent & Normal To A Curve53 mins
Test your knowledge of Tangents & Normals (Quiz)FREE Class
Tangents & Normals (Concept Builder Class)FREE Class
Few Applications of Gauss's law54 mins
Application of Biotechnology | Concepts - 02FREE Class
Interactive Quiz on Biotechnology25 mins
Application of Biotechnology | Concepts - 0160 mins
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