Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-5470-145
+91 7353221155
Use Coupon: CART20 and get 20% off on all online Study Material
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
OTP to be sent to Change
why it is written "continuous in closed interval and differentiable in open interval" in rolle's and langrange's theorem.?
Functions are usually not considered to be differentiable at the end points of the domain. Thus the wording is as such.
Condition should satisfy the eqn. on applying Roll''s theorem and langranges!
thus it is!
In calculus, Rolle''s theorem essentially states that a differentiable function which attains equal values at two distinct points must have apoint somewhere between them where the first derivative (the slope of the tangent line to the graph of the function) is zero.
If a real-valued function f is continuous on aclosed interval [a, b], differentiable on the open interval (a, b), and f(a) = f(b), then there exists a c in the open interval (a, b) such that
This version of Rolle''s theorem is used to prove the mean value theorem, of which Rolle''s theorem is indeed a special case. It is also the basis for the proof of Taylor''s theorem.
Get your questions answered by the expert for free
You will get reply from our expert in sometime.
We will notify you when Our expert answers your question. To View your Question
Win Gift vouchers upto Rs 500/-
Register Yourself for a FREE Demo Class by Top IITians & Medical Experts Today !