Q. 8

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

Condition (1):

Since, f(x)= x3+3x2-24x-80 is a polynomial and we know every polynomial function is continuous for all xϵR.

f(x)= x3+3x2-24x-80 is continuous on [-4,5].

Condition (2):

Here, f’(x)= 3x2+6x-24 which exist in [-4,5].

So, f(x)= x3+3x2-24x-80 is differentiable on (-4,5).

Condition (3):

Here, f(-4)= (-4)3+3(-4)2-24(-4)-80=0

And f(5)= (5)3+3(5)2-24(5)-80=0

i.e. f(-4)=f(5)

Conditions of Rolle’s theorem are satisfied.

Hence, there exist at least one cϵ(-4,5) such that f’(c)=0

i.e. 3c2+6c-24=0

i.e. c=-4 or c=2

Value of c=2 ϵ(-4,5)

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
Practise Questions - Application of Derivatives45 mins
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)52 mins
Tangents & Normals (Concept Builder Class)55 mins
Few Applications of Gauss's law54 mins
Application of Biotechnology | Concepts - 0256 mins
Applications of Ampere's Circuital Law44 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