Take Class 12 Tuition from the Best Tutors

  • Affordable fees
  • 1-1 or Group class
  • Flexible Timings
  • Verified Tutors

Rolle's theorem in Calculus explained

27/12/2016 0 1

Rolle's theorem is slightly different from Mean Value Theorem explained as simple as possible

  1. If a real valued function f(X) is continuous over a closed interval [a,b]
  2. Function is differentiable over an open interval (a,b)
  3. And if, f(a) = f(b) (which means if we substitute values 'a' and 'b' to the given function f(x), the corresponding value of 'y' will be same at 'a' and 'b' and obviously the line joining the endpoints will have ' zero' slope or in short, this line will be parallel to 'X' axis)

Then there exists at least one point 'C' such that derivative OR dy/dx=0 at that point 'C'  or in simple words if we draw a tangent to the curve at point 'C' that tangent will have zero slope or tangent will be parallel to 'X' axis.

Ex: f(x) = x2+2  over [-1, 1]  since this function is a polynomial,  function is continuous between [-1, 1] and differentiable over the interval (-1,1). Here f(-1) = 3 and f(1) = 3 ie: value of 'y' at x= (-1) and value of 'y' at x= (1) are equal. For this function if we join the endpoints of the curve from x = -1 to x = (1) , this line will have 'zero' slope. Now if you differentiate this function wrt to 'X'    y'= 2X. At what value of 'X'   y' =o ?  Yes !!  It is at 'X' = 0. So for this function the point 'C' is at 'X'= 0. Means if we draw a tangent to this curve at x=0, tangent will have zero slope or tangent is parallel to 'X' axis.



0 Dislike
Follow 0

Please Enter a comment



Karthik | 02/01/2017

Well explained. Hope to see more such lessons preferably with sketchs wherever possible.

1 0

Other Lessons for You

To solve any mathematical problem follow the steps as stated below. Read the problem clearly to identify the information provided and the part to be solved. Represent the data or information you read...

How To Record Sale Of Services On Account In Quickbooks?
Keeping track of sales is a critical need for any business, and the QuikBooks accounting packages allows for easy tracking and accounting of the sales and payments made. Sales can be recorded by creating...

Khushboo B.

1 0

Introduction To Accounting: Part 13: Money Measurement Concept
According to the Money Measurement Concept, only those transactions and events are recorded in the books of accounts which can be measured in terms of money. Therefore, a transaction which cannot...

Vedic Mathematics for finding square of a number whose unit place carries 5
As we learned from my previous lesson i,e; (In case of two 2-digited numbers whose digits in 10's place are same and sum of the digits in unit places is 10 For example:- 38 and 32 (10's place digits...

Naimish K.

0 0

Details about New School Classroom Poster - Questions for Building Your Brainpower.
Details about New School Classroom Poster - Questions for Building Your Brainpower.

Looking for Class 12 Tuition Classes?

The best tutors for Class 12 Tuition Classes are on UrbanPro

  • Select the best Tutor
  • Book & Attend a Free Demo
  • Pay and start Learning

Take Class 12 Tuition with the Best Tutors

The best Tutors for Class 12 Tuition Classes are on UrbanPro

This website uses cookies

We use cookies to improve user experience. Choose what cookies you allow us to use. You can read more about our Cookie Policy in our Privacy Policy

Accept All
Decline All

UrbanPro.com is India's largest network of most trusted tutors and institutes. Over 55 lakh students rely on UrbanPro.com, to fulfill their learning requirements across 1,000+ categories. Using UrbanPro.com, parents, and students can compare multiple Tutors and Institutes and choose the one that best suits their requirements. More than 7.5 lakh verified Tutors and Institutes are helping millions of students every day and growing their tutoring business on UrbanPro.com. Whether you are looking for a tutor to learn mathematics, a German language trainer to brush up your German language skills or an institute to upgrade your IT skills, we have got the best selection of Tutors and Training Institutes for you. Read more