Question 126
A polynomial $P(x)$ of Degree $n \ge 3$ has $n$ Real Roots $x_1 \lt x_2 \lt \dots \lt x_n$ such that $x_2 - x_1 \lt x_3 - x_2 \lt \dots \lt x_n - x_{n-1}$. Prove that the maximum of the function $y = |P(x)|$ on the segment $[x_1, x_n]$ Is attained at a point belonging to the segment $[x_{n-1}, x_n]$. Polynomial $P(x)$ degree $n \ge 3$ It has $n$ real roots $x_1 \lt x_2 \lt \dots \lt x_n$, and $x_2 - x_1 \lt x_3 - x_2 \lt \dots \lt x_n - x_{n-1}$. prove that the maximum function $y = |P(x)|$ on the segment $[x_1, x_n]$ is achieved at a point belonging to the segment $[x_{n-1}, x_n]$.