Q. 74.5( 2 Votes )

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



Answer :

Condition (1):


Since, f(x)=x3- 7x2+16x-12 is a polynomial and we know every polynomial function is continuous for all xϵR.


f(x)= x3- 7x2+16x-12 is continuous on [2,3].


Condition (2):


Here, f’(x)=3x2-14x+16 which exist in [2,3].


So, f(x)= x3- 7x2+16x-12 is differentiable on (2,3).


Condition (3):


Here, f(2)= 23- 7(2)2+16(2)-12=0


And f(3)= 33- 7(3)2+16(3)-12=0


i.e. f(2)=f(3)


Conditions of Rolle’s theorem are satisfied.


Hence, there exist at least one cϵ(2,3) such that f’(c)=0


i.e. 3c2-14c+16=0


i.e. (c-2)(3c-7)=0


i.e. c=2 or c=7÷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
Tangent & Normal To A Curve53 mins
Test your knowledge of Tangents & Normals (Quiz)FREE Class
Interactive quizz on tangent and normal, maxima and minima43 mins
Interactive quiz on maxima and minima48 mins
Tangents & Normals (Concept Builder Class)FREE Class
Few Applications of Gauss's law54 mins
Application of Biotechnology | Concepts - 02FREE Class
Application of Biotechnology Part 229 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