Q. 14

It is given that

Answer :

Rolle’s theorem: If f: [a, b] R is continuous on [a, b] and differentiable on (a, b) such that f(a) = f(b), then there exists some c in (a, b) such that f’(c) = 0


Now, Given Rolle’s theorem holds for


f(x) = x3 – 6x2 + ax + b in [1, 3] and for


Now, f (1) = f(3)


(1)3 – 6(1)2 + a (1) + b = (3)3 – 6(3)2 + a (3) + b


1 – 6 + a (1) + b = 27 – 54 + 3a + b


-5 + a = 27 + 3a


2a = 22


a = 11


As there is no equation for b, so b can take any values.


Also, f’(c) = 0


As, f(x) = x3 – 6x2 + ax + b


f’(x) = 3x2 – 12x + a





= 0


So, for any value of ‘b’ and a = 11, the given equation will hold rolle’s theorem in [1, 3]


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
caricature
view all courses
RELATED QUESTIONS :

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