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
I need a prove of this result , it a NCERT question .
if f(x) is continous in [a,b], and f'(x)>0 in (a,b), Prove that f(x) is increasing in [a,b].( please note the closed nature of the interval ) i feel this is a application of langrange mean value theorem or intermediate theorem. PLease help
As f(x) is both continuous and differential...we can apply lagranges theorem
by formula it is sure that for f'(x) to be >0 , b-a should be >0...............
So,a is at lower pt. and b is at higher point..............and hence a increasing function......
f'(x)=f'(b)-f'(a)/b-a....
You are right b-a>0
but how u reach this point that b is a higher point ( i mean f(b) ) and a is a lower point ,
You are inherently using the result that if f'(x)>0 the function is increasing
hence , b is a higher point and a is a lower point
and how come
f'(x)= (f'(b)-f'(a) )/ (b-a) ???
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 !