Rijul saini wrote:
Indian Postal Training Set 2, Problem 1
A polynomial $P (x)$ with real coefficients and of degree $n \ge 3$ has $n$ real roots $x_1 <x_2 < \cdots < x_n$ such that
\[x_2 - x_1 < x_3 - x_2 < \cdots < x_n - x_{n-1} \]
Prove that the maximum value of $|P (x)|$ on the interval $[x_1 , x_n ]$ is attained in the interval $[x_{n-1} , x_n ]$.
http://www.artofproblemsolving.com/Forum/viewtopic.php?t=366260
http://www.artofproblemsolving.com/Forum/viewtopic.php?t=363321
http://www.artofproblemsolving.com/Forum/viewtopic.php?t=364564
http://www.artofproblemsolving.com/Forum/viewtopic.php?t=363287