Answer :

Rolle’s Theorem states that, Let f : [a, b] R be continuous on [a, b] and differentiable on (a, b), such that f(a) = f(b), where a and b are some real numbers.Then there exists some c in (a, b) such that f’(c) = 0.

We have, f(x) = x3 – 3x

Since, f(x) is a polynomial function it is continuous on and differentiable on

Now, as per Rolle’s Theorem, there exists at least one c , such that

f’(c) = 0

3c2 – 3 = 0 [ f’(x) = 3x2 – 3 ]

c2 = 1

c = ±1

c = 1

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