Answer :

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.
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

Verify the Rolle’Mathematics - Exemplar

The value of c inMathematics - Exemplar

For the function Mathematics - Exemplar

Verify the Rolle’Mathematics - Exemplar

Verify the Rolle’Mathematics - Exemplar

Discuss theRD Sharma - Volume 1

Using Rolle’s theMathematics - Exemplar

Verify the Rolle’Mathematics - Exemplar

State True Mathematics - Exemplar

Discuss the appliMathematics - Exemplar