Answer :

Condition (1):

Since, f(x)=e-x (sinx-cosx) is a combination of exponential and trigonometric function which is continuous.

f(x)= e-x (sinx-cosx) is continuous on .

Condition (2):

Here, f’(x)= e-x (sinx + cosx) - e-x (sinx – cosx)

= e-x cosx which exist in .

So, f(x)= e-x (sinx-cosx) is differentiable on

Condition (3):




Conditions of Rolle’s theorem are satisfied.

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

i.e. e-c cos c =0

i.e. cos c = 0


Value of

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