Please solve this question with explanationI am not able to solve these type of questions

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.

take h(x)=sinx, so that h”(x)= – sinx

so, we get sin((x1+x2+....+xn)/n)=sin(pi/n)>=(sinx1+sinx2+.....+sinxn)/n

so, the greatest value of the sum turns out to be n*sin(pi/n), and it occurs when each xi=pi/n