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
Suppose is a twice differentiable, real-valued function on an interval and that for all . Then, for every positive integer m and for all points in , we have
Moreover, equality holds if and only if . A similar result holds if
for all except that the inequality sign is reversed.
now, if we set h(x)=sinx, h’(x)=cosx or h”(x)= – sinx. it is given in question that x1, x2, …..xn lie in the interval (0,π). in ths interval, sinx is positive, implying h”(x)
so, h((x1+x2+...xn)/n)=sin(π/n) >= (sinx1+sinx2+....sinxn)/n
so, the greatest value of the sum turns out to be n*sin(π/n), which occurs when all xi’s are equal to each other.
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 !