# Verify Rolle’s theorem for each of the following functions: Condition (1):

Since, f(x)=sin3x is a trigonometric function and we know every trigonometric function is continuous.

f(x)= sin3x is continuous on [0,π].

Condition (2):

Here, f’(x)= 3cos3x which exist in [0,π].

So, f(x)= sin3x is differentiable on (0,π).

Condition (3):

Here, f(0)=sin0=0

And f(π)=sin3π=0

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. 3cos3c =0

i.e. i.e. 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  Tangent & Normal To A Curve53 mins  Test your knowledge of Tangents & Normals (Quiz)52 mins  Interactive quizz on tangent and normal, maxima and minima43 mins  Interactive quiz on maxima and minima48 mins  Tangents & Normals (Concept Builder Class)55 mins  Few Applications of Gauss's law54 mins  Application of Biotechnology | Concepts - 0256 mins  Application of Biotechnology Part 229 mins  Interactive Quiz | Biotechnology - 0342 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 