Q. 105.0( 2 Votes )

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

Answer :

Condition (1):

Since, f(x)=(x-1)(x-2)2 is a polynomial and we know every polynomial function is continuous for all xϵR.

f(x)= (x-1)(x-2)2 is continuous on [1,2].

Condition (2):

Here, f’(x)= (x-2)2+2(x-1)(x-2) which exist in [1,2].

So, f(x)= (x-1)(x-2)2 is differentiable on (1,2).

Condition (3):

Here, f(1)= (1-1)(1-2)2=0

And f(2)= (2-1)(2-2)2=0

i.e. f(1)=f(2)

Conditions of Rolle’s theorem are satisfied.

Hence, there exist at least one cϵ(1,2) such that f’(c)=0

i.e. (c-2)2+2(c-1)(c-2)=0


i.e. c=2 or c=4÷3

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 - 0256 mins
Application of Biotechnology Part 229 mins
Interactive Quiz on Biotechnology25 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