Q. 1

# Verify Rolle’s th

Answer :

Condition (1):

Since, f(x)=x2 is a polynomial and we know every polynomial function is continuous for all xϵR.

f(x)=x2 is continuous on [-1,1].

Condition (2):

Here, f’(x)=2x which exist in [-1,1].

So, f(x)=x2 is differentiable on (-1,1).

Condition (3):

Here, f(-1)=(-1)2=1

And f(1)=11=1

i.e. f(-1)=f(1)

Conditions of Rolle’s theorem are satisfied.

Hence, there exist at least one cϵ(-1,1) such that f’(c)=0

i.e. 2c=0

i.e. c=0

Value of c=0ϵ(-1,1)

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 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