Calculus Level 3

Given that $$f(x) = a_0 + a_1 x + a_2 x^2 + \ldots + a_n x^n$$, and $$|f(x) | \leq | e^{x-1} - 1 |$$ for all $$x \geq 0$$. Find the value of $$y$$ if $$y \geq |a_1 + 2a_2 + 3a_3 + \ldots + n a_n |$$.

×