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