Q. 1 K4.0( 2 Votes )

Verify Lagrange’s

Answer :

Lagrange’s mean value theorem states that if a function f(x) is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there is at least one point x=c on this interval, such that


f(b)−f(a)=f′(c)(b−a)



This theorem is also known as First Mean Value Theorem.




f(x) is continuous in [1, 3]



Differentiating with respect to x:





Here,



f’(x) exists for all values except 0


f(x) is differentiable in (1, 3)


So both the necessary conditions of Lagrange’s mean value theorem is satisfied.






On differentiating with respect to x:



For f’(c), put the value of x=c in f’(x):



For f(3), put the value of x=3 in f(x):





For f(1), put the value of x=1 in f(x):



f(1) = 2







6(c2 – 1) = 4c2


6c2 – 6 = 4c2


6c2 – 4c2 = 6


2c2 = 6



c2 = 3



Hence, Lagrange’s mean value theorem is verified.


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